What is it about mobile phone chipsets that makes the unsuitable for a TV stick or STB?
Is it that there is special TV-specific hardware like tuners, HW accelerated audio and video decoders, and PQ/AQ accelerators?
Apple has adapter their A15 chipsets for use in the Apple TV, so it seems possible. But obviously the Apple TV products don't have tuners, aren't driving a display natively, and probably don't have enough I/O interfaces to add all the extra hardware you'd need to embed it in a panel or STB.
It's a good question and I'm not actually sure as I'm not a hardware guy, just a user who's looked into these productz. So far, the popular Android TV set-top boxes (or sticks) I've seen use SoCs that seem dedicated to set-top applications. It may that mobile phone chipsets have different integration to support cellular modems and air interfaces.
There are some boxes which use use Android instead of Android TV but these tend to require using versions of the streaming apps made for mobile phones. I haven't really looked into these as they tend not to work well with remote controls so I haven't been interested.