The amount of mostly unintentional (by the user) data transfers is out of hand.

If your corporate site, where you advertise your new high-end TVs and laptops, starts triggering warnings in all your visitors' browsers that it might be associated with malware and falling off all the SERPs for similar reasons, you're going to stop loading it with junk pretty quickly (and its trust score will improve pretty quickly as a direct result). Likewise, if your smart device tries to phone home and home has acquired negative rep, maybe that connection gets blocked automatically at the firewall.

We'd need a system that was guided by interested/aware participants who are unlikely to be successfully gamed and that mostly "just worked" for average users, but we've managed to build those in other contexts before so it doesn't seem completely out of the question.

As long as they rely on your own network for their external connectivity, you can always firewall them (at the expense of any connected features you do want to use, perhaps, but then I suspect most of us would agree that 99% of those are junk in most smart TVs anyway and be OK with that limitation).

The problem comes when they can form their own connections, but in that case they're not under your control anyway, DoH or not.

Pi-Hole has a nice GUI, but if you already have openwrt, dd-wrt or pfsense, you can likely just install packages.