Is there any UK/JAA license or a rating that needs a "cross country" time?
The
FAA PPL, IR and CPL all need it.
I think that is the real answer to the question: why are you logging time? Usually one is logging time for a specific objective, and one has to make sure it is right for that objective.
That's why it can be important to get the instructor to sign the logbook entry. In years to come you may be glad you did that 2 hour x/c dual VFR flight, or whatever, but the instructor will be long gone (he's a first orificer on a 737 probably) and without the signature the flight will be unverifiable.
That said, I have never had unsigned entries queried; under FAA, the instructor you fly with before the test in question willmake sure you can actually do the stuff.
In the absence of a specific other requirement, I would recommend everybody making sure they have
FAA compatible logbook entries
That's where the future lies.