Rather than assuming it is because of JAA, CAA or FAA rules you need to understand why people do their training in the first place.
I know some people who trained just so they could prove they had the ability. Once they passed it was mission accomplished, thanks very much, bye.
People's financial circumstances change, some quite dramatically, either through work, health, marriage/divorce.
People's priorities change, too, either through marriage/divorce, health, moving etc.
Then there's the external "motivation" -- the hard-sell of PPL training from clubs/schools right up to when the test is passed. Once you're licenced unless you own an aircraft or share, schools will hire you aircraft but only if they're not needed for PPL training that day -- planning/booking lessons is easy in comparison to planning/booking the hire of school aircraft...
IO540 talks a lot about the state of rental aircraft -- and he's right. What is acceptable to a keen student might not be seen in such a good light by a nervous passenger. Once the wife/girlfriend has said "no" (because the aircraft is so old and ropey and
looks "dangerous") there's a strong incentive to stop, and spend the money flying in a brand-new Easy/Ryan B737
There's also the choice of destinations available to fly to commercially for <£50. Where it previously made economic sense to learn to fly so you could take your wife/girlfriend/kids (whatever) on holiday or off the beaten track somewhere, the likes of Easy/Ryanair etc have bought commercial flying costs down to far less than you could fly there yourself -- and Ryanair particularly will take you to off the beaten track destinations
I don't believe the blame for 100% of the dropout rate can be laid at the door of the regulator. Somewhere along the way individuals have choices to make, and those choices might not include spending £100 to grab a burger from a soggy airfield in the middle of nowhere.