vik 

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 could 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.