What about Reuben sandwiches? Many of the non-Kosher Jewish delis in NYC offer them. I've always thought that Jewish delis and Kosher delis could co-exist (though obviously NOT in the same space!)
In my mind, a Reuben is diner food. As for delis, I associate Jewish Delis with my grandparents, who were ALL kosher. Just the smell of smoked meat that hits you when I walk into a deli has me thinking "kosher"- and by that, I mean NO DAIRY- even if said deli is not Kosher (like Katz's).
I do not, have never and will never keep Kosher. But some things are just ingrained in me- and one of them is milk with meat. It actually repulses me. Deep seeded Jewish guilt perhaps? There are exceptions, of course, the biggest of which is cheeseburgers. Yes, I understand that this makes absolutely NO sense, but very little of the human psyche does. If that human is a New York Jew, then all bets are off.