Doesn't DoH eliminate caching as well? It means all your queries go out to some server on the internet with perhaps 20-50ms of latency, instead of a local cache potentially on your LAN with <1ms. A DNS cache on the LAN would also merge queries from multiple devices, concealing which device is making the query and in many cases preventing the query from having to be sent over the internet at all.
The best thing might be to have internet gateways run a DNS stub that itself makes queries via DoH/DoT/whatever and then caches them for every device on the LAN. The gateway is typically the DHCP server so it can hand itself out as the DNS and requires no configuration as well. And then it works across all devices and applications.