There can be so many dis-advantages of this approach, few are below-
As user rights are managed in mysql in myisam tables, so if you will insert users very frequently then locking can be here.
Privileges will not be effective till you flush them, and flush command lock the tables and can block all you application queries for some time.
You can't save additional important information of user in these system tables, while in your own user table you can save user name, email, creation time, password update time etc.
Easy management as you can create limited profile in mysql user table and map a group of users with these predefined profiles.
By this you can allow a user to connect db but restrict to do some specific task in applicatioin as you can join this tables with active/inactive status in you queries.