Why it will often not be considered a cheesesteak is that over the years the term cheesesteak has and will be related to the concept of Philadelphia cheesesteak. There are a few exceptions. I have a lifetime of experience with one cheesesteak that is different than a Philadelphia cheesesteak but Piccolo’s in Hoboken has been serving a <<<Hoboken>>> cheesesteak for over 50 years and I dare someone to get yappy at Piccolo’s about the cheesesteak served there.
You’re in PA where customers are very likely to expect an authentic version of a Philadelphia cheesesteak.
If regs in PA allowed raw meat to be served from a standard hot dog cart…I’d think there would be droves of them all over PA.
There are some carts in NYC that serve cheesesteaks but they are not serving them from hot dog carts….and they use pre-cooked meat.