I agree that this is a very complicated problem that played a roled in the rise of NoSQL. Given it isn't the only reason for the rise of NoSQL but it contributed. This problem is worse when development teams and DBAs database do not report to the same person. Good luck convincing a DBA about your change. Disclaimer, I have the utmost respect for DBAs.
I agree with that. If your database doesn't care about a "schema", there usually are no operations available which change the schema of your data. Unfortunately that also means that if your database doesn't consider the schema its problem, when you do finally want to change the implicit schema of your data, it becomes the dev's problem.