While CAT I is approved, other CAT's are in the approval phase with the FAA and others.
FAA/ICAO don't even have all the relevant standards for CAT II/III GBAS (GAST-D) published yet, so it's impossible for them to approve anything. The required standards probably wont be in place until next year at the earliest. Only then can manufacturers have designs evaluated for formal approval, and
that process will probably take at least another year.
Also, in the US, currently GBAS is not funded by the FAA so the airlines have to pay for everything (ground equipment, site installation, flight testing, aircraft avionics upgrades, operations, etc.) I think after doing cost/benefit analysis, they are happy to just stick with CAT I GLS for now and are not in a hurry implement GAST-D.