Using T&T turn rules all the time?

A couple weeks ago I played a 2v1 game and we used the triumph and treachery rules (random card pull) for taking turns and I feel like it added an element of surprise every turn. Even in a 1 on 1 game I think it adds variance to the game and can make for some really strong turning of the tides if someone goes the second half of turn 3 and then the first half of turn 4 or something along those lines. Has anyone else done something similar to randomizing player turn order on each turn after the first (this is usually decided by the scenario/deployment)?  Could do cards like t&t or even just a heads up dice roll to determine which player goes first for each turn. I’m intrigued to try it out but curious if anyone sees an obvious hang up with doing this or if they tried it and how it worked in their group. Thanks in advance for the input.