Westy,
I too hate the idea of personal data being publicly available. All that would be required would be the minimum to associate your means of identification with the record of your flying licence. For example by typing in a pilot's name, address and licence number would cause the CAA's machine to reveal pertinent details about your licence.
"some pilots fly to faraway places where internet actually doesn't exist!"
True, I guess there are a few settlements providing aviation facilities to strangers which are beyond economic reach of the public telephone network. But once there, it's probably a bit late to start worrying about whether a pilot is licensed or not.
In any event, how often would a Patagonian flight-ops actually know whether the piece of paper I held under his nose was a genuine JAR-FCL licence, or something I printed myself? Without the benefit of internet access to Pprune, I doubt he would even know what colour the cover should be.