JAA did not change anything in practice.
Pre-JAA, if you had a German PPL and you were flying a German-reg plane, you could fly it worldwide VFR, as usual. If you had an IR on that German PPL, you could fly that D-reg worldwide IFR (as usual).
All basic ICAO stuff. License = aircraft reg => worldwide flying privileges.
What JAA gave us was the ability to fly e.g. a D-reg plane on a UK issued JAR-FCL compliant PPL, and fly it worldwide.
How many pilots take advantage of that, I don't know. Some surely do.
On mutual license recognition, ICAO asks for this, but almost no "major" country actually does it. All of them run various protection rackets.
EASA is taking things a bit further than most, well into the 3rd world police state area, by forcing pilots to have EASA papers (in addition to the ICAO-required) purely according to the operator's residence, even if the EASA-required papers are not themselves valid for that aircraft.