Howa, my reasoning is slightly different.
If C is required to give the minimum required level of safety it is clear that VFR are required to be separated from IFR.
The only way of providing this separation safely when the aircraft are not visual to the controller is by using approach radar ie primary and secondary.
Class C under the US NAS requires approach radar. We have a similar standard of living to the USA and a similar high value of life - then we can afford a similar level of safety equipment.
Class C without radar is a sham as a VFR aircraft can transit the airspace without detection by ATC.
Why thinking controllers would want C without radar and adequate staffing is beyond me.
Maybe they consider their jobs as some type of charity position.