Just look to IPv6 to see how well that approach has worked?
To me the issue the people are advocating for WRT DNS is the centralization of DNS services, so many customers concentrated with such few providers.
I really don't see anything wrong with DNS as it is.
Certainly doesn't have to be that way, nothing in DNS prevents people from running their own DNS, though bigger companies are probably best off with a Dyn or Neustar to be able to absorb those DDoS attacks better. Obviously pretty much any internet provider has a DNS service available, and in many cases they may not even charge for the service since for the most part it doesn't cost much to run unless you're needing very regular updates assuming they don't have a UI to manage DNS.
I've run my own personal authoritative DNS since 1996 myself (still do today).