To make it easier for the public to see a (I think "their" was given up) GP, either GPs have to have less of their time demanded for other things - a steady rise over 14 previous years and several previous to those - or there need to be more GPs.
Appointment systems don't.
And a system which resembles a lottery at 0800 not at all.
(An advance and one which a quality engineer might look at, is to arrange to know what happened at the end after each call to a practice.)