Not old at all. Almost every TV sold in the US with an ATSC receiver (so most mid to high end) will also do NTSC (and "clear"/unencrypted QAM-64/256 for cable) In the past decade it became more common for low cost TVs to drop the tuner entirely. These use jellybean tuner/demod parts and you tend to get the whole batch or nothing at all, once you have RF in, demodding NTSC is basically free.

Most TVs with a tuner can still listen to analog signals, I'm assuming for legacy device support (game consoles, VCRs, etc.)

My mom kept around her old two in one TV with a VCR because she didn’t feel like digitizing a bunch of old VHS tapes. Glad she did because it’s fun to play the Nintendo and use a C64 on it :)

Every one of them must and should have a coaxial cable input.