How many applications actually do, though? At most places I've worked it's common to integrate a schema migration tool (flyway, liquibase) that requires DDL, and I've never seen anyone go to the effort of splitting out an ephemeral instance to run the migration with a separate database connection configuration.
Anecdotal but we certainly run flyway migrations with a high privelage user not the regular low privelage "app" user who can only SELECT UPDATE and sometimes DELETE. The fact that nobody does this doesn't mean it's a bad idea just a reflection on poor industry practice (add it to the list)
Oof, I never let the application alter the tables. Makes running some applications a giant pain, but DDL should be an administrative thing, not a runtime thing.