Studies have been done! Here is the latest one, for psilocybin. The mystical experiences are deeply related to therapeutic outcome https://www.frontiersin.org/articles/10.3389/fphar.2022.8416...
Here is the first one I am aware of: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3050654/. So 14 years of evidence backing up this claim.