I was thinking it might be more compelling with a multiplayer element. Two players take turns picking or freezing on a bigger grid.
Yeah for sure! You could even make a pretty simple AI, since the decision isn't about where you pick, just if you do or not.
One thing that might be useful inspiration for developing this: It's basically a press-your-luck game, which have been heavily explored in the tabletop space. A couple notable examples are Can't Stop, No Thanks and Incan Gold.