Not sure if its national, but in the Midwest, we have Naf Naf Grill, which is like the Chipotle of middle eastern food. Delicious by fast food standards, and I don't get why middle eastern / mediterranean food isn't bigger in the US. And to your point specifically, Indian food seems like it would fit the same template really well!

Curry up now exists. There's not many but they are growing.

It’s called Tandoor.

They exist. They’re just not chains.

It’s common to have a lunchtime buffet that simply puts out curries and charges for access to the table. Just not convenient for takeout since curry is tricky to transport.

I once heard about a system around Mumbai where one village routinely cooked lunches (curry, rice, etc), and ferried them via metal tankards by train to a neighboring town/city where people were working.

Roti is pretty much the Indian Chipotle, but it's so-so.

Closet I can think of is Masala