If I had to have ONLY three bikes, they had to be current models, and from the same manufacturer... Yamaha it would be
Yamaha FJR1300
Yamaha T7 (ok not available in states yet... but europe)
Yamaha YZ250X
KTM might be able to do it.. but they dont really have a sport touring bike. But I could do one of the big KTM adventures, a 500EXC-f and a 300 XC-W. Three bikes are all kinds of compromises.....
But I cant imagine only three bikes hitting all the categories for me. I need a proper dirt bike, a dirt worthy dual sport, sport or naked sport bike, sport touring bike, trials bike, and some sort of adventure bike (preferably middle weight).
With that list, Honda would be the only one to be able to check off all the boxes, and there would be some compromise choices still.