This is something that realy intrigues me. Is it a mere coïncidence that psychedelic substances like DMT stimulate neurogenesis, or is there a link between neurogenesis and psychedelic effects? From the point of view of someone who likes psychedelics, it is tempting to believe that there is such a link.
But ofcourse that doesn't make it true.

I would realy like to hear the opinion of people who're professionally involved in neuroscience or biochemistry on this.

Feel free to speculate.

Yes, there is a lot of evidence showing that psychedelics cause neurogenesis. Enough evidence in my opinion that one could say NOT taking natural psychedelics is irresponsible for personal health.

Here is some reading on the subject:

1.- Basic intro but with some reference to papers https://www.psymposia.com/magazine/do-psychedelics-trigger-neurogenesis-heres-what-we-know/
2.- Ayahuasca discussion from the Beckley Foundation
3.- Salvinorin A patent with data on improved neurological trauma recovery in this post.

Folks here could come up with a much more comprehensive list, this is just an appetizer. Would be interesting if someone presented a comprehensive review of the literature, at the moment this is not so easy due to the recent attack on open science by business interests.

But is it just a lucky coïncidence, or is the effect that psychedelics have on neurogenesis related to their immediate psychological effects?

I can see why there would be a direct link, but this is pure speculation: The brain is constantly producing information. In the predictive coding model that i've discussed before, these are predictions but i think the basics of this is true in other models as well...there is a mechanism that corrects for the innevitable errors. The classic psychedelics such as DMT temporarily shut down this mechanism, so the 'fantasizing' mechanisms of the brain can run free uninhibited.
This error detection mechanism is needed for survival, but it makes sense to assume that for learning and growth, we realy need to use the fantasize mode.
After all, variation is the motor for growth in all living things. This is so in the evolution of species, but it is also true on the levels of individuals.
If you want to become better at whatever skill you're practising, you need to try new things and new aproaches.
When i play darts, i know how to throw pretty accurately. But if i want to get better, i need to deviate from what i know.

So i can imagine that there is a link between the 'fantasy mode' and neurogenesis. But maybe there are better explanations for why it works.

In the case of salvia there was measured improved blood circulation in the brain which helped the tested animals recover more quickly from nervous system damage vs the control.

There are other natural plants that are clearly neuroregenerative and not psychedelic: lions mane being a good example.

However, maybe expanding ones cultural thought patterns (or having them explode) may also help the brain if simply from being a good mental work out.

The subject is so complex that who really knows? There could be several different reasons for the observed positive effects. At the end of the day we have the papers and testimonials showing consistent personal improvements thanks to the use of psychedelics.

Plants can do all kinds of things. When we ignorantly make them illegal or ignore them at the altar of Western arrogance we suffer for it. I'm reading an interesting book "Return to the Brain of Eden" that discusses how a lot of our modern problems and cognitive disfunctions could be rooted in diet changes through our recent evolution.