I wondered this as well when I was shopping for a new TV a few years ago. Unfortunately, not only is it really difficult to find a "dumb" modern TV, but the best display panels will always be on smart TVs because that's what sells.

That said, I ended up getting a Sony A95K 55" TV, and it's been great. It has Google TV built-in, but I immediately connected our Apple TV to it, and it's never seen the Internet since. No nags, either. Sony also made it really easy to disable motion interpolation, a feature I really dislike.