I've never worked on a system where we didn't make an effort to make sure we were NOT dependent on a specific DB vendor/implementation and avoiding SP's has always been a part of that.
I expect at some point we'll have a similar initiative around cloud providers.
This is pretty good since one can generally fast unit test DB code with an embedded database.
The Oracle version had a lot of logic written as SP. I migrated them to MySQL SP.
So the conclusion is: SP don't make it impossible to migrate from one database to another, and second: yes database migrations do happen.
Also: all database migrations I have known involve Oracle in one way to another. Oracle salespeople are way too nosy.