Correct me if I'm wrong, but the concern I have about browser-controlled DoH is that it seems like it could make it harder for a tech-savvy user to assert control over their own network. IIRC, most network-level ad-blocking operates at the DNS level. I've also personally blocked telemetry by setting my router's DNS proxy to resolve certain telemetry servers to 0.0.0.0. It's my understanding that DoH would bypass that. Couple that with Google's planned neutering of Chrome's ad-blocking API, and it seems like it will become increasingly hard for end-users to avoid ads.
And the fact that DoH uses HTTP seems like it would make it impractical to block as a protocol.
I think I would have preferred an encrypted DNS protocol that ran on its own port, at least.