I think that making all scrimmages ranked, or even putting a minimum number of matches, still wouldnt solve all of the problems with the system.
If all matches were ranked, you wouldn't be able to send/accept only ranked matches you know you'd win, but you'd still be able to manipulate your ELO by sending more ranked challenges to teams you can/cant beat, or teams you know who are helping you manipulate your score.
Especially if the only-ranked matches system allowed auto-accepting matches, you just keep re-sending matches to them that you know the outcome of until they stop auto-accepting. But if you don't allow auto-accepting, then the scrimmage system will be super slow, having to wait until players log on and notice the request.
Forcing them to have 10 ranked matches (or any arbitrary number) wont quite solve the problem, either, as it's still easily possible to get your 10 by manipulating the system.
The core problem is that, if players are allowed to choose where/how to setup their ranked matches, they will generally choose to do it in the way that maximizes their own score. That, by definition, is gaming the system.