Peer-to-peer networks are easy to overthrow completely even with a relatively small number of malicious nodes.
> Also it's hierarchical P2P, so if you control the root servers, you control the naming system. It is decentralized only to aid availability and resilience.
ICANN only controls delegation to TLDs.
> I want free names for 10 websites.
I want free beer.
> Such a naming system would be outside the immediate control of governments, therefore democracy has nothing to do with it.
In the real world people care about ownership disputes, protecting trademarks, accountability and other legal matters.
> This still uses DNS, and does not solve anything.
Actually, it does. DNS solves everything just fine.