It doesn’t work with psycopg or many other libraries that use c extensions. That’s the main reason.
Edit: things seem to have changed since I last looked into compiling a dependency for pypy. https://doc.pypy.org/en/latest/faq.html#do-c-extension-modul... now says they support c-extension modules without modifications
The package you mentioned, some postgres thing apparently, mentions they support pypy 3.9 and 3.10: https://www.psycopg.org/psycopg3/docs/basic/install.html
But maybe even with that, it's unable to support some extensions?