I both sympathise with the loss of the bike and the police's disinterest. My last bike was stolen from my work place and although not worth a great deal and being fully comp - it's the inconveinience and hassle.
When I initially phoned the police to report the crime they refused to give me a crime number unless I first pledged them money from my own pocket if my insurance company refused to pay them £105 recovery fee and £12 per day storage.
They also said they would not treat it as a crime because it was probable children under 16, so P.A.C.E. (police and criminal evidence act) meant they were unlikely to get a conviction.
As it turned out my workmate found it torched on his way home and the company let me borrow the works van to transport it, so the police got no money off anyone - Shame!
Unfortunately we live in a country where even though we pay their wages we seem to be there to serve them and not the other way around.
Without knowing the full circumstances of your situation, it is difficult, if not impossible to generalise (unlike your eminent generalisation above) & I doubt you're necessarily after an explanation,
But, to try.......the reason the Police seek to establish whether someone is prepared to pay a recovery fee, is because it is not (generally) the Police who recover stolen vehicles. It is contracted out to Recovery Agents. Having found stolen vehicle's & due to the lack of ability on the part of the owners to collect them vehicles were being re-stolen & the Police held responsible....ie. the losers ( in every sense) expected the Police to guard their vehicles until they felt like collecting them & when they didn't/couldn't they blamed the Police & sued. (It's Taxpayers money that pays the bill.)
Similarly, in these days of frequent vehicle abandonment, there are unscrupulose sorts who, finding them in possesion of a totally knackered vehicle drive it to the next town / borough ....lay by, give it a good kicking, or torch it & get it disposed of at someone else's expense....ie. the Taxpayer (again).....ie. most of US. Abandoned vehicles are the Local Authorities responsibility to dispose of, ie. hazardous substances, rubber, plastics, fluids, 'scrap' & quite often, a vehicle reported stolen, collected at the Taxpayers expense is abandoned by the owner because they never intended to collect it as (if they have insurance) they were after a payout & if they haven't they can't be ar*ed. Again......the tab is picked up on the rates.
So, to the issue of being asked IF you are sufficiently interested in the bike to be prepared to pay for it's recovery, that is an entirely reasonable question. Whether they were "blackmailing" you for the sake of a Crime is somewhat 'incredulous'....as I said earlier, ALL Forces have Vehicle Crime as a 'reduction target'. If some unscrupulous Forces are seeking to under record then that is an Integrity issue & you should have complained, initially up the Supervisory ladder & if necessary to the Professional Standard's Department.
As for not recording it because there was a presupposition that it was a Juvenile offender.............that is utter bo**ox.....both ways up, they say communities get the Police they deserve.....not sure how that fit's with the response you've had.
Hardly good luck to find it burnt out, but if you hadn't....how could you know that it wasn't going to be found 300 miles away, not just around the corner ?? it would still have had to be collected & protected until you or your insurers were in a position to collect it.....it wouldn't have been the Police that got the money, it would 'almost certainly' have been the Contractor, & he's on call 24/7, has a compound, vehicles & staff to maintain............& would have been hoping your insurers would be meeting the costs anyway ?
Unfortunately, the Police don't have a Crystal Ball, or a sixth sense, or X ray-eyes.