I'm curious: did you consider using Flask as a back-end, instead of parse-server? Is parse-server just easier than coding your own API back-end with Flask and whichever db you like?
No. That would effectively mean reimplementing all the logic of parse-server in flask. And when I was done doing that, I wouldn't have a client library in every language ready to interact with my backend.
Parse-server is definitely a faster way to start because it's already an API layer in front of the database.