It’s not something I do. Hence - can I have one without a touchscreen?

Framework does sell their parts piecemeal, so if you were inclined once new parts are available, you could put together one to your liking without a touchscreen.

Eg - Current Framework 13 bottom stand alone https://frame.work/products/bottom-cover-kit?v=FRANFD0001

I guess not. A touchscreen is cheap anyway, compared to many other components.