The Venn diagram for psychedelics include escapism, but it includes a lot more as well. Psychedelics can be a powerful tool, and for all the good that they can bring you, they can also wreck your shit for a while. It really depends on who you are, what context you take them in and what you do afterwards. This applies more broadly to other substances as well, even ones not typically seen as psychedelic, like alcohol and caffeine. There can be therapeutic effects with those as well.
For example, if you're feeling really stuck at a certain point in life and you take the time to get drunk by yourself and listen to some enjoyable music, you can end up being really honest with yourself and become aware of what you need to do to get unstuck. But you can also get drunk at a party and make a number of bad decisions that you'll regret later. It be like that when it comes to psychedelics as well.
Imho, the main benefits of psychedelics are two-fold.
One has to do with subjective experience - psychedelics can simply provide you with a different experience, a different point of view. This can help you see that there are other possibilities for the narratives you tell yourself and this can be beneficial. Depression is a good example here - it's super easy to forget what it's like to not be depressed and psychedelics can provide a temporary clarity about it that can later help get out of the depressive state.
The temporary difference in point of view can also cultivate more skepticism in general. This is especially true for certain "truths" we hold about ourselves (like insecurities, inadequacies, fears). Psychedelics can open us up to consider different causes for our behaviours and this can be therapeutic as well. But I gotta say, they can also make you lose yourself within a new false narrative, so skepticism is a powerful ally here.
The other benefit simply has to do with neuroplasticity. Most psychedelics open up a dose-dependent learning period that lasts from days to weeks. That's why something like a shroom trip doesn't really end until a few weeks after the shroom is ingested, when that learning period eventually closes. Even if you didn't experience anything spiritually or psychologically significant in the acute phase of the trip, you can still benefit greatly from the learning window that opens up afterwards.
It's a good time to try a new activity, do some self-reflection, change a habit, have a therapy session or two, connect with people on a deeper level. You might be surprised by your learning abilities after a shroom trip. But I gotta say, all this also opens you up to learning "bad things" too, so again, skepticism helps here.
Yeah, you can do all that without psychedelics as well, but there are a couple of problems here - you might be unaware that there's something you can actually do, and even if you are, you might not know what to look at or how to change your point of view about it. Psychedelics can provide a strong emotional and psychological example that can guide you in that process.