Stealth Pilot wrote:

you really only need C, D and G.

c - full time atc above 10,000ft with mandatory radio
d - part time atc with mandatory radio even when the d is shut
down(ctaf)
g - free airspace to 10,000ft


So no full-time ATC below 10,000 MSL? Why?


For reference, here are the ICAO airspace class descriptions:

ANNEX 11 TO THE CONVENTION ON INTERNATIONAL CIVIL AVIATION


CHAPTER 2. GENERAL


2.6 Classification of airspaces


2.6.1 ATS airspaces shall be classified and designated in accordance
with the following:


Class A. IFR flights only are permitted, all flights are provided with
air traffic control service and are separated from each other.


Class B. IFR and VFR flights are permitted, all flights are provided
with air traffic control service and are separated from each other.


Class C. IFR and VFR flights are permitted, all flights are provided
with air traffic control service and IFR flights are separated from other
IFR flights and from VFR flights. VFR flights are separated from IFR flights
and receive traffic information in respect of other VFR flights.


Class D. IFR and VFR flights are permitted and all flights are provided
with air traffic control service, IFR flights are separated from other IFR
flights and receive traffic information in respect of VFR flights, VFR
flights receive traffic information in respect of all other flights.


Class E. IFR and VFR flights are permitted, IFR flights are provided
with air traffic control service and are separated from other IFR flights.
All flights receive traffic information as far as is practical. Class E
shall not be used for control zones.


Class F. IFR and VFR flights are permitted, all participating IFR
flights receive an air traffic advisory service and all flights receive
flight information service if requested.


Note.-- Where air traffic advisory service is implemented, this is
considered normally as a temporary measure only until such time as it can be
replaced by air traffic control. (See also PANS-RAC, Part VII, 1.4.1.2.)


Class G. IFR and VFR flights are permitted and receive flight
information service if requested.