I don't know how other people use it. But for me, that's their central function. And their redesigns have sometimes made that more difficult.
The current version is okay. One of their previous versions hid the search bar somewhere else, and that was very annoying.
As for the rest of the site, I've never used it.
I can see how that's confusing, though, since it's a different use case than what we associate them as having.
Because it's not default, and learning how to tweak a browser isn't fun to me. I'd rather study history, or how to write well.
I also have an irrational sense that bypassing someone's website is wrong. By avoiding their homepage, I'd also be avoiding their plea for donations, for example. But I realize this is an irrational feeling, and the only reason I'm voicing it is because you asked why I personally won't do that.
They've spent a lot of effort on improving playback and media discovery, and on the contrary, I've heard a lot of positives.
If there's some specific or large deviation from their mission that you perceive from their re-design, I'd like to hear it. I have a great interest in internet preservation, and even though I'm not associated with IA, I would hope to learn more about how people are using the collected work of organizations of the IA and how to better serve those people.