I’m guessing (not sure) that AltGr, visible in the picture, switches between the two options like Shift would. Shift still switches case.

I think the main reason they didn’t make an umlaut modifier is that ä is considered a distinct letter from a. It would be like asking why have a key for w (“double u”) when it could have been typed as uu. Not a perfect analogy but the best I can think of right now.