It would not be a 5-10 minute wait though. Maybe during peak hours, but other times of day might see 15-30 minutes wait. Every game. Hope nobody dodges or misses a champion lock-in.
Not enough people play support, so untill that issue gets fixed, everyone else has to bite the bullet and do it from time to time.
You might not mind a little bit of a wait, but that's not feasible if you wake up early, and have time for one game before getting ready for work/school when you suddenly need to put 75-90 minutes aside for a single game (hour games are rare, but they do exist still).
Non-supports having to play support isn't a new thing. It's always had to happen due to the lack of Support players. It's likely not going away anytime soon either.