Personally, I'd enjoy mechanics just happening at random times in the fight with each one having an internal cooldown (like how us as players have cooldowns for our own skills). A super simple solution to a problem people bring up (even Yoshida) whenever someone asks for some randomness in the fight.

We have some randomness in our fights already with with certain mechanics having variations within themselves but the fact that almost every fight starts with the healer are-you-paying-attention raidwide is exactly the sort of predictive stuff that I believe is what adds to that feeling of sameness folks want a breath of fresh air from.

Take a boss, allow it to roll its mechanics but give them a CD so they can't do the same mechanic back-to-back-to-back. And maybe make a boss that doesn't have portions where they just auto-attack for a bit. Let them ABC.