It is not true that the medieval rabbis were the first to apply Isaiah 53 to Israel instead of the Messiah. The Israel interpretation is actually very ancient.

It is not true that the medieval rabbis were the first to apply Isaiah 53 to Israel instead of the Messiah. The Israel interpretation is actually very ancient.
You’re partially correct. The earliest reference to this interpretation is found in a second-century Christian source recounting a discussion between a Gentile follower of Jesus and some Jewish teachers who did not believe in him. But aside from one passing reference in Midrash Rabbah (where part of one verse is interpreted with reference to the righteous), a specific identification of Isaiah 53 with Israel is not found in any Rabbinic literature until almost one thousand years after Jesus. (In other words, it is not found in the Talmuds, the Targums, or in the midrashim.) Therefore, the view that Isaiah 53 spoke of Israel can hardly be considered a standard (or ancient) Rabbinic interpretation, and for the traditional Jew, that’s what really matters.
There is really nothing puzzling here at all. The evidence is well known and has been fully accessible for centuries. The Rabbinic data is as follows:
     Targum Jonathan interprets Isaiah 52:13–53:12 (which, for simplicity in this discussion, we will simply call Isaiah 53) with reference to the Messiah, despite the fact that the Targum virtually rewrites the entire passage, changing the verses that speak clearly of the servant’s sufferings so that they speak instead of the suffering of the nations. This means the Messianic interpretation of the passage must have been quite prominent when the Targum was being formed, since it would have been much easier to not add the explicit reference to the Messiah (in 52:13) rather than to virtually rewrite the verses that seemed to contradict the expected role of the Messiah.131
     The Talmud interprets various verses in this section with reference to righteous individuals within Israel (including the Messiah) but never once with reference to the nation of Israel as a whole.132 The Jerusalem Talmud (Shekalim 5:1) applies 53:12 to Rabbi Akiva, while the Babylonian Talmud applies 53:4 to the Messiah in Sanhedrin 98b, 53:10 to the righteous in general in Berakhot 5a, and 53:12 to Moses in Sotah 14a.
     Midrash Rabbah interprets 53:5 with reference to the Messiah (Ruth Rabbah 2:14), while interpreting 53:12 with reference to Israel in exile (Numbers Rabbah 13:2). This last interpretation, offered in a passing interpretation of Song of Solomon 5:1, is the one and only time in the first thousand years of recorded Rabbinic literature that any portion of any verse in Isaiah 53 is applied to Israel as a nation.
     Yalkut Shimoni (a thirteenth-century compilation of earlier midrashic writings) applies 52:13 to the Messiah, stating that the Messiah—called the great mountain according to the Yalkut’s interpretation of Zechariah 4:7—is “greater than the patriarchs … higher than Abraham … lifted up above Moses … and loftier than the ministering angels” (2:571; see also 2:621). Isaiah 53:5 is applied to the sufferings of “King Messiah” (2:620),133 while 53:12 is applied to Moses (2:338), as in the Talmudic passage referred to above.
Reviewing the above evidence, one thing is clear: The ancient rabbis—traditional Judaism’s most authoritative sources—almost always interpreted Isaiah 53 with reference to an individual rather than to Israel as a whole or to the righteous within Israel, and this individual was most commonly interpreted to be the Messiah. Once again, I cannot underscore how important this is for a traditional Jew, nor can I emphasize enough how this fact has largely been obscured by later interpreters: The Messianic interpretation was common among the ancient rabbis! As we noted above (4.6), even Rabbi Saʿadiah Gaon, the renowned leader of Babylonian Jewry in the ninth century, who did not interpret this chapter as Messianic, still follows the individual interpretation of the passage, explaining it with reference to Jeremiah. Surely, if the national interpretation had been common, he would have endorsed it, especially since it would have helped him in his polemics against the Christianity of his day.
The first authoritative recorded instance of Isaiah 53 being interpreted with reference to national Israel is found in the commentary of Rashi (eleventh century), who interpreted it, however, in terms of the righteous remnant of Jacob. Not surprisingly, Ibn Ezra (twelfth century), who also read Isaiah 53 as speaking of the people of Israel, began his comments with the words, “This is an extremely difficult passage.” But when we read it with reference to Yeshua, it is not difficult at all. Rather, it is wonderfully clear, giving the reader the distinct feeling that the chapter was written after the Messiah’s crucifixion and resurrection. Despite the fact that Rashi, Ibn Ezra, and Radak (twelfth to thirteenth century) as well all stated that the servant of the Lord in Isaiah 53 was national Israel (or the righteous remnant within the nation)—rather than the prophet himself or the Messiah—many other Jewish commentators, even in our day, still claim that the servant of the Lord in Isaiah 53 is the Messiah.
As stated above (4.6), the only ancient reference of any kind to the national interpretation of Isaiah 53 is actually found in a non-Jewish source, namely, a polemical work entitled Contra Celsum, written by the second-century Christian scholar Origen. In this work Origen refutes the arguments of an opponent of both Judaism and Christianity named Celsus, and while discussing Messianic prophecies, Origen makes reference to a disputation he once had with some learned Jews, stating that the Jews interpreted Isaiah 53 in terms of Israel’s national suffering:
Now I remember that, on one occasion, at a disputation held with certain Jews, who were reckoned wise men, I quoted these prophecies; to which my Jewish opponent replied, that these predictions bore reference to the whole people, regarded as one individual, and as being in a state of dispersion and suffering, in order that many proselytes might be gained, on account of the dispersion of the Jews among numerous heathen nations. And in this way he explained the words, “Thy form shall be of no reputation among men;” and then, “They to whom no message was sent respecting him shall see;” and the expression, “A man under suffering.”
Origen had an immediate reply to this line of interpretation:
Many arguments were employed on that occasion during the discussion to prove that these predictions regarding one particular person were not rightly applied by them to the whole nation. And I asked to what character the expression would be appropriate, “This man bears our sins, and suffers pain on our behalf;” and this, “But He was wounded for our sins, and bruised for our iniquities;” and to whom the expression properly belonged, “By His stripes were we healed.” For it is manifest that it is they who had been sinners, and had been healed by the Savior’s sufferings (whether belonging to the Jewish nation or converts from the Gentiles), who use such language in the writings of the prophet who foresaw these events, and who, under the influence of the Holy Spirit, applied these words to a person. But we seemed to press them hardest with the expression, “Because of the iniquities of My people was He led away unto death.” For if the people, according to them, are the subject of the prophecy, how is the man said to be led away to death because of the iniquities of the people of God, unless he be a different person from that people of God? And who is this person save Jesus Christ, by whose stripes they who believe on Him are healed, when “He had spoiled the principalities and powers (that were over us), and had made a show of them openly on His cross?”134
Outside of this one lone reference—from an ancient Christian source, not an ancient Jewish source—there are no ancient Jewish references to this national interpretation, an interpretation that does not become prominent until the biblical commentary of Rashi, who wrote more than four hundred years after the completion of the Babylonian Talmud.
From this survey, it should be clear that your objection is completely unfounded.

131 Cf. the discussion in Levey, The Messiah, an Aramaic Interpretation; see further Pinkhos Churgin, Targum Jonathan to the Prophets, repr. with Leivy Smolar and Moses Aberbach as Studies in Targum Jonathan to the Prophets (New York: Ktav, 1983).
132 The question raised by the Ethiopian eunuch in Acts 8:34 (while reading Isaiah 53:7–8)—“Tell me, please, who is the prophet talking about, himself or someone else?”—is in keeping with this line of reasoning and is completely consistent with the most obvious meaning of the text.
133 This interpretation is in the midrash to Psalm 2:6, dealing with the Hebrew word nasakti, interpreted here to mean, “I have woven him,” with reference to Judges 16:14, i.e., “I have drawn him out of the chastisements.” R. Huna, on the authority of R. Aha, says, “The chastisements are divided into three parts: one for David and the fathers, one for our own generation, and one for the King Messiah; and this is that which is written, ‘He was wounded for our transgressions, etc.’ ” See Driver and Neubauer, Fifty-Third Chapter of Isaiah, 2:10, for the translation.
134 Origen, Contra Celsum (i.e., Origen Against Celsus), bk. 1, chap. 55 (5:218).
Brown, M. L. (2003). Answering Jewish objections to Jesus, Volume 3: Messianic prophecy objections (58). Grand Rapids, Mich.: Baker Books.