OK Terry, since I have never bought a hot dog from one of these vendors, my opinion is just that, my opinion.
People put anything on hot dogs, but true NYers put mustard and sauerkraut, and basically that's it. yes the vendors have these onions and they are great. I have eaten them at home as they sell them prepared in the stores.
I guess it is just personal likes or dislikes. Myself, I like mustard AND ketchup AND a dollop of horseradish sauce. I can then have some relish, (I have this jalapeno stuff that I love),and then top it off with some of said onions or sauerkraut, but I never mix them together.
Hope this helps