Welcome to the forums! 
That’s certainly an idea.
Or, as a less drastic of a change to ults across the board, they could just revert/rework Mercy with Mass Rez + Tweaks and work with it from there, since Mass Rez originally took care of punishing bad ult economy from the start.
Also, I’m not sure if putting everyone’s ults on a cooldown is a good idea. Some ults are too strong to be so common, and others don’t benefit from being on a fixed timer. There would have to be a lot of compromises for such a system I feel, and it may make the game a lot less rewarding to play (with the lack of building your ults and whatnot), IMO.
~Sincerely Yours xoxo,
a Lover of True, Fair, and Fun Balance.
xavvypls 