Why doesn't ADS-B use satcoms like ADS-C?
It's already here, but it's private

Your proposed geostationary orbits are very high, and since aircraft are the transmitters, that means high power antennas are required from the aircraft.

However, low Earth orbits (LEO) are more forgiving. By using 72 ADS-B receiver-equipped satellites in LEO (icao.int), Aireon will provide 100% global coverage by Q3 2018 (aireon.com).

This requires no change to the existing ADS-B technology as long the antenna is top-mounted and capable of 125 watts (most airliners already support 200 W). But it is not a free service to ATC units. Interested ANSPs can use Aireon's data to supplement their own surveillance for a fee. NAV CANADA will use their services for the North Atlantic region by Q4 2018, for example.

The power demand and the provider being a private entity, explains the why not. If surveillance is meant to be publicly owned by each government to be in control of the data source, then each country will need its own constellation of satellites – sort of like the countries and regions that are launching their own GNSS constellations.

Slide 16 (shown below) is from the linked icao.int presentation. The presentation also explains how ADS-C is different:


  ADS-C is an Alternative, But Has Limitations
  
  
  ADS-C tracking is not comparable to ADS-B surveillance
  Slower ADS-C update rates results in higher separation (mins vs. sec)
  Barrier to entry: ADS-C requires costly installation and subscriptions
  Multiple providers require individualized equipage on aircraft
  Several commercial aircraft types can’t be retrofitted
  Almost no coverage over polar regions for certain providers
  No service is provided to unequipped aircraft