We probably could, but it would take a lot - a lot - of work.
I'm not sure you could rework Tryndamere in a way that would appeal to his current players without:
a) keeping the ultimate in some form
b) keeping him somewhat mobile
c) making him primarily auto attack based
Which is pretty tough if you also want to solve the problems people playing against him have.
I can't think of many people who would be happy with Tryn's ultimate staying (although it does have some counterplay - disengage and re-engage)
Some deeper systems changes will be needed (e.g. an item system to support melee auto attackers/light fighters - items to help them stick that the opponent can play around, a sufficient mix of offence and defence in a way that Juggernauts, tanks and assassins won't like and more).
Reworking Tryndamere successfully will require a lot more work than other champions, and he isn't exactly priority 1 at the moment.