My son, unexpectedly, has gotten attached to Toca Store -- he remains indifferent to most of the rest (or perhaps just hasn't gotten hooked; it can be hard to tell) and will play it either by himself or with R. at least once a day.
The remainder of this post is largely about elimination and iPad apps. You've been warned.
Because the Bird in Miny Moe Car reminded me that preschoolers reliably like elimination humor, I went searching for more of the same. Dog Park involves a dog which has a couple of status bars. Essentially, the dog has to drink from things like ponds/lakes/water fountains and pee on fire hydrants and similar. There are other dogs. There can be a competitive aspect if you use the multi-player aspects of the game, which we do not. There are multiple settings. A. finds it amusing and has returned to it, altho I'm pretty sure she doesn't really get the status bars yet and finds the make-the-dog-drink a lot less interesting than the make-the-dog-pee aspects of the game.
I also picked up Potty Panic HD, however, it's a little too abstract for the kids. Essentially, you have to line up people in desperate needs with available potties -- or disaster strikes. I hesitate to recommend it, but I can see where it could be addictive for certain people. I don't like any games in this category (I discovered that after trying one of the farm panic versions a while back), so it's hard for me to tell whether one is a good/mediocre/bad instance of the type.
I feel like there are probably more games out there that mine elimination humor for entertainment, but I'm not finding them. There _are_ a startling number of potty training apps, and an even more surprising number of movement-tracking apps (including ones that will help you calculate just how much you are paid for the amount of time you spend in the loo, assuming you are salaried). I have not bought any of them.