I don't think it is user share so much as fundamental problems with
Alternate DNS systems.

How easy is it to block alternate DNS by governmental, law, or other
agencies or actors?  Unlike the existing DNS system, it is quite trivial to
flatten an entire alternate DNS and have no appreciable impact to the
Internet.
How does it work at sites that block outbound DNS requests at the edge?
Are you and all those you want to access these resources technical enough
to configure all your phones, computers, etc. to implement alternate DNS
for all networks?
Why trust an alternate DNS?