"Uncontrolled" airspace is a funny term. It has nothing to do with the presence or absence of control towers, or whether an aircraft's flight path is being "controlled" by someone other than the pilot.

All that "uncontrolled" airspace really means is that ATC doesn't provide separation for IFR traffic. Pilots are ALWAYS responsible for "seeing and avoiding" traffic when flying VFR, but IFR separation is provided by ATC when flying in controlled airspace.

If you mean there will eventually be no UN-USED airspace -- that's a different matter!