Thanks!
I feel like there is room with some of these systems (basically any of them with a decent recharge method) to find a good compromise on global vs. fighter-only maneuvers, especially common ones like disarm, etc. One of the complaints WotC wanted to address in the latest packet is some players not wanting to sacrifice damage in order to perform maneuvers. I like that trade-off, but I can understand those who do not. And in any case, the current fighter lost at least some charm in addressing this concern. Maybe "combat rhythm" will permit an acceptable compromise, giving broader access to maneuvers while allowing fighters to remain special and not face the damage vs. maneuver tradeoff.
With combat rhythm the choice is spending dice vs. not spending dice, and extra damage isn't the default any more than tripping is. Because the risk of losing the dice for future rounds is always present one can't spam it, so it is a special bonus over the default attack. (And this it shares with the current packet.)
Other combatants, however, could give up weapon damage dice to perform basic maneuvers. Which is fine since these classes don't specialize in using maneuvers, or ever learn them in any proper sense without multiclassing or possibly some feats. A Paladin with 3 weapon damage dice is, at best, as good with maneuvers as a fighter with 3 weapon damage dice and no combat rhythm (i.e. a fighter having bad luck). A fighter with any combat rhythm dice is strictly superior: more powerful maneuvers are possible, maneuver use is more flexible, the tradeoff is more favorable (base damage unchanged), and barring some bad luck the fighter is likely to maintain these advantages for a great deal of the fight.
This might also support a nice conceptual separation between classes for the purposes of improvised maneuvers, by letting the fighter pay for those from the combat rhythm pool, and making other classes use weapon damage dice. The fighter can be a superlative improviser, but other classes can still try things. In a sense if you're not a fighter you are improvising, and I think that is a thematically satisfying perspective. (Contrast that to expertise dice as a universal martial mechanic, where the fighter has trouble standing out to many people even if they have all sorts of advantages within the system.)
(The usual unresolved issue is this: can one "improvise" an existing maneuver the fighter hasn't specifically learned, or reuse improvised maneuvers. The solutions, besides ignoring the situation entirely, are either to impose an additional penalty on improvised/unlearned maneuvers or not to have "learning a maneuver" be a game concept. The latter seems unlikely in D&D, but I think we can do the former well. When improvising the fighter has disadvantage on the attack for the purposes of retaining any combat rhythm dice spent. The attack itself is not penalized, the chance to retain combat rhythm dice is only moderately penalized, and the fighter is still better off than any non-fighter. Nevertheless, there is a clear incentive to train in maneuvers one plans to use with any frequency.)