The Press Turn system works great because it takes a tired, mundane gameplay mechanic (elementary mechanics) and blows it up into a life-or-death situation.
In most games, elemental weaknesses just amount to slapping the correct choice of several spell options in order to score a little extra damage. But Press Turn makes elemental weaknesses into a HUGE deal -- it would be really tough to win in SMT III/DDS without getting extra turns and blocking enemy moves (by nulling their attacks). There's a lot of tactical decisions you have to make as a result -- how to arrange your characters and attacks in order to maximum the number of turns you get and avoid losing any turns (e.g. first take out an enemy that nulls fire, then you can hit the remaining ones with a fire spell that targets all of them). Each different configuration of enemies calls for different tactics. And because there are SO many element/status types in Megaten, there's also a strategic element of how to assemble your team & abilities so that you can effectively target enemy weaknesses (often this calls for shuffling of party members/abilities to match a given area!)
Don't see what could be annoying about it, really.