Mountain biking of any type not just downhill racing is certainly one application. Road racing/sport riding when not racing would be a couple more. Touring on rough/poor/unpaved roads. Winter riding. Commuting on poor roads.
You can get around some of the problems with small wheels with suspension, but that adds cost and complexity to the bike so you can't say a large wheeled rigid bike is pointless by comparison.
I use different sized wheel bikes one after the other on a daily basis and there certainly are benefits to small & to larger wheel sizes.
If you wanted to say that for non-competitive use on nicely paved roads you do almost anything with a small wheeled bike I'd agree, but that doesn't mean large wheels are useless since I could say the same thing for large wheel bikes and they have the benefit of tackling poor roads/dirt roads and off road better.
Suspension tires don't add cost or complexity. As I said in the OP the only argument against wide suspension tires is weight, but small wheels negate it so there's no argument against them at all.
All my riding is on rough, poor roads with a good amount commuting in winter and I don't see what the advantage of larger wheels are. They just make those wide tires I need heavier.
Dirt/off road sure (there are many strange contraptions which are useful in the wilderness), but it's very hard to see any useful purpose in such riding for the 99% of mankind that lives in civilization, hence, larger diameter wheels are pointless. You can't say the same in reverse because small wheels have many advantages while large wheels have only one esoteric advantage at the fringe of a bicycle's capability. If riding off/unpaved road had a point then the bicycle would have been invented shortly after the wheel instead of thousands of years later during the rise of modern civilization.
Large wheels are only have advantage for sport; in other words diversion; in other words pointless.