Sounds pretty reasonable.

Within the US, there are at least two major diner chains:

https://www.dennys.com/

https://www.ihop.com/en

At a diner in America, I'd be unsurprised to see some less "diner" offerings. When I go to my local non-chain diner, I order fettucine alfredo. And the article here has a good picture of a diner advertising "American and Korean food". I think part of the core diner concept is a somewhat athematic menu that is meant to cater to local tastes.

With that in mind, Cheesecake Factory might also be thought of as a diner. https://www.thecheesecakefactory.com/menu

So I'm a little surprised at the idea of a diner that only has classic burgers / shakes / pancakes, but I'd have to admit those are fairly core dishes.

I'd say a waffle house is a better chain if you're in the lower Southeast. Much closer to a true diner experience