I don't see how this is even relevant. What do MySQL's limitations have to do with your decision to store a password hash? Are you writing your entire application in MySQL?
I'm curious - is that a common practice with backend applications - writing only with MySql application code and not using anything else like Java/PHP/Python/C# etc?
I know Oracle has pretty sophisticated stored procedures, but even so, most of the application logic of systems I've seen had program code written in an "external" language.