There have been various attempts at alternative DNS root [1] by people unhappy with ICANN.
In the past, these attempts haven't been able to convince ISPs to point their users to the forked service - even if they mirror every existing domain free of charge.
And you don't just have to convince domain registrants and end users; you need to bring mailserver administrators and certificate authorities along too.
I'm not saying it's impossible - Google could force things unilaterally with a change to Chrome, for example - but history shows users are slow to vote with their feet.
We don't even need the majority of the world to start using them, we just need browsers to add support.