It connects areas of your brain that have never connected before. Maybe your geometric recognition connects with your creativity and you become aware of realities that you once never knew. As a great psychonaut once said; "Acid opens up doors, but once they're open, you can't close them".
A lot of people don't like to use drugs in general. Hallucinogens are still a big mystery to science. Just from the fear of the unknown they shouldn't be recommended on the scale you're suggesting. There are recorded cases of them causing irreversible changes in healthy adults.