Unless management "sees the light" and fully backs you in bringing order into chaos you're going to lose. It works and they haven't had problems they're willing to address.

Try for incremental changes such as formal review of new databases/tables that require the DBA team sign off on them. That might be enough of a start to move things along.

If management isn't going to actively and consistently support you then don't give yourself an ulcer. Realize you're going to be living with that environment going forward. Then decide if you want to work there.