Yeah, approval is a weird sort of thing. Technically, both my characters need approvals; Gark needs a 2nd (ever) and Unit 16 needs both a judge and a 2nd for his recent level (so that he can then level up AGAIN - guess I might as well do that first, actually). But I haven't been pressing for them because Unit 16 isn't even in a game, and Gark's game isn't going to be finishing up anytime too soon. So the need for them to get those approvals at this exact moment is low.
Maybe we need some kind of ranking system? Certain people need to bubble up to the top due to starting / finishing games, while others who are just sitting around aren't in much of a hurry. Or is "pestering judges" pretty much the ranking system for now, and that's probably good enough?