"Eileh pekudei hamishkan, mishkan ha'eidus..." Rashi comments that the Mishkan is called "mishkan ha'eidus", the tent of testimony, because it was built to stand as a testimony to the fact that Hashem forgave Bnei Yisrael for the sin of the eigel.
The meforshei Rashi ask why the mishkan in particular was needed to testify to Hashem's forgiveness of Bnei Yisrael. Didn't the fact that Hashem gave the luchos a second time demonstrate his forgiveness? Maharal in Gur Arye offers two answers:
1) Torah is a necessity; it doesn't demonstrate the added love that comes with forgiveness. Let me give you an analogy: Can you imagine a parent boasting of the love he/she shows for his/her child by providing that child with food, with water, with a room to sleep in (I'm thinking of a Harry Potter-like crawlspace)? That's not love -- even prisoners in Alcatraz get that much! These are basic necessities for survival. In the same way, Torah is our chiyus, it's necessary for our survival as well. Mitzvos lav le'henos nitnu -- Maharal explains elsewhere that mitzvos are supposed to be a burden. I don't think he means that mitzvos are not supposed to be enjoyable, but rather what he means is that the motivation to do mitzvos should not be personal enjoyment. Mitzvos should be done out of a sense of necessity, because we can't live without them, just as we can't live without eating, drinking, breathing.
The giving of the luchos was necessary simply to ensure the survival of Klal Yisrael -- we cannot exist without Torah. The Mishkan demonstrated that added gift of Hashem's love.
2) Midrashim compare the sin of the eigel to an act of infidelity committed by a bride on the day of chupah/kiddushin. A sotah, a woman who has been unfaithful, is not permitted to live with her husband. To show that our sin was forgiven, Hashem had to show that he could again live with us again in the same home. The Mishkan is that shared home -- it is the dwelling place for the Shechina and ourselves.
Implicit in this answer is the assumption that Torah alone is not a testament to the presence of the Shechina. In other words, a person can be involved in Torah and still not be connected to the Shechina. The truth is that Chazal already tell us that there can be a disconnect between learning and being close to Hashem: Halevay osi azavu v'torasi shamaru... Hashem says that so long as we don't abandon Torah, even if we abandon him, we will find a way back -- clearly, one can have a connection to Torah without having a connection to Hashem. The former may lead eventually to the latter, but they are not one and the same.
It's not enough to connect to Torah alone; we need to build that dwelling place to share with the Shechina.