I had the same view until I tried dmt. With dmt, you can easily find a "break through" dose. This is the point where your consciousness stops being a disinterested spectator and gets sucked into the experience. The moment your consciousness gets pulled in is extremely disconcerting, I'd never felt anything like it (including other psychedelics).

The resulting experiences are basically religious visions (I'm an atheist). Often, an entity appears and reveals a vision.

> Maybe it's that psychedelics also induce feelings of having discovered something important, and a lot of people don't try to double-check whether they actually did.

I think psychedelics solidify or clarify feelings or ideas that you previously had. Lots of people take them as evidence of their superstitious feelings. For me, not being superstitious, they did not have that effect but they did clarify my worldview.