People should just say what they mean here. DNSSEC is in fact a server-to-server protocol, and your response is "yes, you should just run your own servers".
Fact check: A resolver is not restricted to servers, and DNSSEC is not restricted to server-to-server traffic.
Ah, yes. What even is a "DNS server"? Clearly it's not the thing that shows up in your network configuration under "DNS server"; that, as you observe, is properly labeled "resolver".