Separation services (at least for some aircraft) are most definitely provided on area frequencies!
Take a look at a (say) VNC chart legend.
What we are talking about are the wide green lines, which are
Class G FIA ("Area") frequency boundaries. Within those volumes from the surface up to the base of CTA a Flight Information Service is provided,
not a separation service.
Wide dashed brown lines are
Class E airspace boundaries, on which a separation service is provided to IFR aircraft.
In some instances the frequency used is the same, but the service in the volumes is in accordance with the airspace classification.
See AIP definitions for "Area VHF" and "FIA".