This is kinda what I do. I personally really enjoy Gmail and don't find any competitor can match it, especially since I use a catch-all domain and really value having Gmail's spam filtering in place. However I use my own domain and have all my email forwarded to Gmail. If I ever get locked out of my Gmail account I can just switch where my email is going and be good to go.
I also do regular Google Takeout backups so that I at least have access to the majority of emails and google data.