One might make the case that Shavuot is really the end of Pesah, just like Simhat Torah is really the end of the High Holidays, on the opposite side of the Jewish calendar. And, curiously enough, they are both about the Torah: Shavuot is when we commemorate the Israelites' receiving of the Torah at Sinai, and Simhat Torah is when we celebrate the completion of a full cycle of Torah reading, and go back to the beginning again.
It's not a coincidence. In reinterpreting the Jewish Festivals, which are essentially agricultural in their unadorned Torah-based origin, the rabbis sought to overlay their new Jewish model: that of learning as the fundamental basis for Judaism. Without a Temple, without a centralized sacrificial cult, they reasoned that prayer and ritual would go only so far to keep Jews connected, and particularly when they were no longer living agrarian lives. Studying and interpreting ancient texts, however, made them instantly relevant.
As such, each of these two major holiday clusters concludes with a celebration of Torah. The message is clear: What will sustain us from spring to fall and from fall to spring, without a major holiday in between? Taking the words of Torah to heart, and dwelling on them constantly. Citing the words of Joshua (1:8):
This verse became a battle-cry for the rabbis, embracing the study of Torah as the life-force of the Jewish people. The Torah and its millennia of interpretive work are not an afterthought, but rather the focal point for day-to-day Jewish existence.לֹא-יָמוּשׁ סֵפֶר הַתּוֹרָה הַזֶּה מִפִּיךָ, וְהָגִיתָ בּוֹ יוֹמָם וָלַיְלָהLo yamush sefer haTorah hazeh mipikha, vehagita bo yomam valaila
Let not this Book of the Teaching cease from your lips, but recite it day and night...
Rabbi Seth Adelson