In which way are they a monopoly? Is that US specific? In the UK/EU there are at least half a dozen different tractor brands which I could name, all of them with significant market share.
John Deere limits your options with regard to repair. It's not so much a monopoly as it is anticompetitive
AGCO has like 1/5th of the farm equipment market in the US. Massey-Furgeson and Allis-Chalmers being their big two tractor brands.
I don't think a brand being fashionable, to a middle aged demographic, makes them a monopoly. They're just popular. There are plenty of other similar bikes that can be bought.
edit: I'm an idiot. I read the comment as being about Harley Davidson.
John Deere doesn't make bikes. They make tractors and farm equipment.
My bad. I just realized I read the comment as Harley Davidson rather than John Deere.