To be fair, who would really say that they got chopped because they were useless?
It would be exceptionally rare for any pilot trainee to be 'useless'. Often the reason for being removed from training is due to something else - such as limited spare mental capacity, reaching a plateau of ability, being unable to progress at the required rate. But rare indeed to be considered 'useless'. Slow learners? A chum was nearly chopped after failing the 'conversion handling check' on the JP5, but later became a top test pilot!
At the end of the old (and excellent) common-core JP course, pilots would be streamed according to their aptitude. Also, FJ streamed pilots who couldn't cope with the Gnat or TWU might find themselves re-streamed to multis - but back in about 1975-6, ME training actually stopped altogether at one stage, so there was nowhere for them to go if they were removed from training at Valley.
In fact you had to have reached the FJ OCU stage to have any chance of being re-streamed in 1976-ish. Some who subsequently went to the Vulcan did an 'asymmetric' course on the Canberra T4 which was about 3 hours of which about 20 min were on 2 engines, I gather! Great fun, or so they said.
You can indeed be 'wrong place, wrong time' if suspended from BJFT, due to the varying ME/RW requirements of the service. One chap I knew never failed a course, but was told that there were no slots available. So he became an Air Trafficker, but successfully fought his corner a few years later and became (I think) a Nimrod pilot.
Self-suspensions are equally rare. One chap I knew scared himself by seeing his cine-gun film of an A/A session against the flag behind Puddy's Meatbox - and the Meteor was in the frame whilst he was still firing. He admitted that he hadn't realised this - so asked to be re-streamed before he killed someone. Another chap simply "wasn't happy" even when tootling along on a perfect summer day at 250ft and 420 kts even if 100% sure of his position - so self-suspended and became an Engineering Officer.
But I've never heard of anyone who soloed in the JP being dismissed as 'useless'.