The possible solutions are pretty limited if you ask me.
We could go with roleq 1-4-1 builds what would require the rebalance of all support and tank heroes. This is still less than the rebalance need on 2/2/2 and would decrease qtimes for dps.
We could go with mirrored roleq setups with vote systems where the matchmaker makes sure the same amounts of roles are present both sides and if a huge majority of the players in the match agree they could vote in role changes, free choices, etc…
Blizzard could go and rebalance all tank+support heroes and release enough of them to be on par with how much dps we have.
The problem in all cases is that Blizzard needs to do huge rebalances, need to throw out true flexing and somehow make support and tank play actually fun.