As a child in 1950s Columbus I was raised on Velveeta, which to my knowledge, was about all we ever had in the house. For the first decade or more of my life, as far as I knew, cheese came in yellow unrefrigerated boxes. I loved pizza but never thought about what the cheese component was. I knew about Swiss and sort of liked it on occasion, but I basically stuck with good old American.
After that I grew to love many real cheeses, but I'm still very happy with American on my hamburger, and I'll ask for cheddar as often as not. I haven't been putting any cheese on hot dogs here so I don't have an opinion as to which I prefer, but I suspect regular American is what you'd get most places. However, we always seem to have pre-grated yellow cheese around for quick and easy melting on things, and that is usually a mild cheddar. That's what I use on my own Cincinnati chili (because I don't see any pre-grated American at my store, and I'm lazy), so I'd probably be okay with it on a cheese & chili & onion hot dog, too.
Never got close enough to liking the blue cheeses. The faintest whiff of gorgonzola in a salad is tolerable, but really, a faint whiff is my limit. But I love many cheeses, and love tasting various and sundry ones when the opportunity presents itself.