In the ‘olden days’ you used to see varying rim sizes on F1 cars as the teams worked with their tyre manufacturers to develop what they thought was the best solution for the car. This was in the days of chunky tyres everywhere in motorsport. The trend for increasingly low profile tyres in sportscar racing really kicked off in the 80s and 90s when they were still using steel brakes with carbon pads, which required huge brake rotors to effectively brake the cars without suffering huge temperature issues. Look at the nineties super touring cars for the best example of this (and if you’re like me, suffer a small pang of nostalgia and lament the sad state of touring cars these days..)
F1 cars adopted exotic brake materials before sportscars and GT racing, so a smaller brake was always a reasonable solution. There’s not really any huge technical advantage to having a high sidewall, other than the inherent suspension characteristics which have their disadvantages as well as advantages. As much as anything else, it’s an aesthetic choice since an F1 car with a low profile tyre would look a bit odd now we’re all used to seeing them with the 13” rims. Obviously since control tyres were introduced, it meant that every car had to have the same sized rims, which in turn standardised a lot of things like damper lengths, wishbone configurations, brake designs, and suchlike (though of course subtle variations are present on every car, depending on their own individual design philosophy).
In order to increase the rim size every car would need to be redesigned for something which would offer virtually no practical benefit other than perhaps reducing the costs of brake materials. Clearly in these days of austerity this doesn’t seem like a particularly attractive solution, though I could see the benefit for the tyre supplier in terms of a greater perception of road-relevance. Perception being the key word here, since clearly an F1 tyre is still going to be an ultra-specialised prototype which would not function correctly on any other type of vehicle.