First, let me clarify the particular problem case:
The client provided an advertised critical control to a
search operation. The server responded with
unavailableCriticalExtension.
I would argue that advertisement implies the server
recognizes and understands the control (that is,
it is 'supported') BUT that the advertisement
doesn't necessarily imply that any particular
operation extended by the control is serviceable.
However, if not serviceable (for whatever reason),
the server should return a service error, such as
unwillingToPerform, not unavailableCriticalExtension.