It also disables their plugins (browsing, code interpreter, etc.)

This is so stupid. I just checked and yeah, that's why Browsing wasn't available for me! I wish their UI wasn't such a mess and it would have told me. I disabled history because I find it annoying that it sticks around and I don't care to use it. I didn't expect this would prevent me from seeing the Browsing plugin. Had I known I wouldn't have disabled it in the first place. Definitely a facepalm moment.

I think that’s intentional. They’re trying to discourage you from opting out.

feels like kind of a fair tradeoff