Ana isnt as good as people believe and once people notice how important she is to the overall OW ecosystem, people wont be so trigger happy on banning Ana.
Specially when Mauga/Hog exist and people cant deal with them without Mauga. People are going to quickly notice how important Ana as a hero that puts the reins on enemy tanks is. Specially for the overall viability of the popular DPS heroes that arent good tank busters, like Genji and Soldier.
If anything, I expect support players to leave in droves because the only support pick that tanks respect gets banned every match. Banning Ana will, if anything, showcase that the support role has little agency to counter the enemy tank, and that tank-busters aside Bastion have been abandoned (Reaper, Mei, Symmetra, Junkrat) and are weak.
Hero bans will be an extremely bad game to be in, but it will quickly showcase all the whiners that you cant just delete entire heroes out of the game without bigger, worse consequences that will make the game worse for them too.