> Wouldn’t a smart tv do something ... smarter than just using the default dns given to it by the network?

It could certainly try... but usually you would block that in your firewall. Fixed DNS servers or fixed server IP addresses are tricky because if you ever need to change them, you can't, because you'd need to update the hardware (which you can't since it sits behind a firewall).

It could try to use things like Google's DNS server, but that is easily blocked in your router.

Not a lot that could be done except trusting your (internal) DNS server...

Why should the programmers of the TV's OS look for edge cases, and do you think the TV makers would give them budget for that? For 90+% of users the standard config of trusting the DHCP server will work fine, and the Pi-Hole users will probably not give them money anyway, and will be dedicated to defeat their workarounds...

I've been worried about companies that make software like this (applications with embedded telemetry or advertisements) starting to do their on DoH style lookups.

I don't KNOW of any doing it but I can't imagine it'd be too hard for them to do.