I agree, this is a problem, but also complicated when you factor in things like captive portal resolution. In my case it was preventing my VPN connection because the upstream router’s DNS did not resolve the VPN address. A custom DNS was configured in the settings, but that only helped the clients not the router itself.
Maybe there needs to be a “switch” in the GUI for this? Something that allows switching the router’s DNS between the upstream DHCP DNS and the custom configured DNS. I think that would solve my problem, but these issues are complex so it’s hard to see whether that solves the problem for everyone or not. I appreciate that you are trying to find a balance between good functionality and an easy configuration experience.