Well, fun for some people... not so much for others. I think I would definitely be one who would have fun and find it interesting, but not sure with the kind of setting that is often considered for a therapy session now. Client lying on a couch with eyeshades and two therapists staring at them for hours. I think that setting would very much disturb (if not destroy) my experience. It should be individualized much more, but it's tricky because nearly everyone would probably prefer a different setting, which people can create when they use drugs on their own, even more in a group retreat like the one I attended (which lasted a week, so enough room for variety), less in a small office.

One main reason behind the "hype" around using psychedelics therapeutically is that the effects have the potential to last long, with minimal direct administration/experience, unlike most established psych drugs that we need to take regularly, long-term. This part needs a lot more research though and there will certainly be a lot of variability between people. Even with ketamine (that we have more data on now), most people need repeated doses and, even then, it may not last very long. The advantage is that when it works, it often works very fast unlike (again) most traditional psych medications, so it could snap someone out of a crisis.

As far as the mood altering properties, the idea is not to prolong the actual psychedelic state - that would not be good for sure. More to use the experience for insight and then apply that to improve one's life (with or without external help). There may also be direct pharmacological after-effects, but that's exactly the area that needs much more research in a clinical setting, because most of the reports about long-term benefits are still anecdotal, even if some of that has hundreds of years of human tradition associated with it.