Anyone can run their own DNS root, but good luck getting people to use it. And ICANN has a history of deliberately colliding with TLDs used by competing services.
Browser vendors and OS makers should do an end run around ISPs and ICANN. Just agree between themselves ( what are they like 10? tops) and fork the current registries. Then issue domains themselves.
What are the plebs gonna do? Go the the non existent alternative?
Google already controls chunks of every platform involved, some of them are very large, (network, domain registry, OS, browser, search engine, web hosting/content delivery) and eats away the importance of domains bite by bite. Non-tech people do not type in domains anymore, they search for them. URLs are getting hidden away further and further.
The DNS resolver is configurable, not hard coded. Forcing a switch would require OS vendors to ignore the resolver issued via DHCP, which would not work on many corporate networks that block outbound DNS not via their resolver.
Yes I think any new system would have to see the old one grandfathered (give the current incumbents time to find something useful to do instead of jetting off to conferences all year).
Browsers/OS would be reasonably easy in most circumstances, but there are embedded devices, load-balancing configurations, other esoteric uses for DNS (text records, mail etc) that'd have to be considered as well.
An attack surface is ISPs and Governments strongarming them to use their own DNS roots which can then be plugged into the "new" root servers conforming with the theoretical browser vendor, os vendor alliance.
What are the plebs gonna do? Go the the non existent alternative?