There are many applications, albeit none commercial for ac, where we are using GBAS for CAT III autoland. While CAT I is approved, other CAT's are in the approval phase with the FAA and others.
Autoland and automatic rollout was possible, but not approved.
Exactly, if one looks at the precision available with GBAS, CAT III autoland is not an issue, you just have to get the regulatory agencies to approve its use.
Just as a turn to final with GBAS is well documented, there are no commercial ac applications. (again, there are a few non-commercial already in use)
We even have RNP AR transition to GBAS final in operation. (military ops)