I've been having fun with Touhou Spell Bubble the past month or so. On top of the classic Puzzle Bobble gameplay, the blank bubble mechanics draw obvious comparison to the back and forth counterplay in Puyo Puyo, while the awakening and counter systems let both players "take turns" trying to make or defend against big plays. Meanwhile, unique character powers and spell cards add some significant character differentiation to add asymmetry to the whole mix.
Since you'd expect to play out the entire chart in a rhythm game without interruption, scoring a KO in TSB just downs the other player and adds a big amount of score to the attacking player. Coupled together with the rest of its gameplay mechanics, the down system is the secret sauce that glues together Spell Bubble's game pace. Amusingly enough, the game I keep drawing comparisons in this regard is actually American Football. In both instances the number of (touch)downs one player leads the other by dictates playcalling decisions and leads to really tense and exciting moments in gameplay.
Of course, Puyo's tried to implement a down system on at least two occasions, one in the pair puyo mode in 20th Anniversary and again in skill battle in both Chronicles and PPT2. Contrary to Spell Bubble, the down system doesn't really feel well implemented in these modes -- the lack of a fixed timer limits the types of play-making opportunities that work well in TSB, and some of the finer details of the way Sega has integrated downs into Puyo gameplay up to the present have led to odd play patterns (often the best strategy is to intentionally SD since the penalty for dying is lower than the one for taking damage from garbage).
Much like the other criticisms I've levied at Sega's non-Tsuu endeavors in the past, there could be a version of the down system in Puyo that ends up being fun and exciting... but what exactly it'd look like is up in the air. Once again I feel like Sega's being held hostage by the success of Tsuu - while it's arguable whether a mainline Puyo game even wants to have a down system, as a spinoff, TSB is allowed the liberty of diverging from the original Puzzle Bobble and experimenting with core mechanics.