FAAJAA.
The FAA do not convert a PPL as you put it, they issue a Restricted PPL on the basis of a JAA or other National PPL. IN the UK it is less onerous than that, you can quite simply fly on your foreign PPL no conversion required.
If a JAA licence holder wants an unrestricted FAA PPL then you have to take Tests, by the same token if a FAA PPL holder wants a JAA licence you also have to take tests, where is the difference. You do not have to convert a licence when you can continue to exercise the privileges of your national licence.
The major problems associated with the JAA are quite simple, underfunding by all States involved. A limited number of people trying to do a mamouth task with little support from the major players and in many cases, with inappropriate qualifications. Throw in a bit of nationalism, no a lot of nationalism, a few political ideals and you finish up with European aviation being run from a Post Office Box in Holland.