Its not a question of PRS not being bothered...
AIUI what they do is a sample from the data they do have and extrapolate it to the rest. Its the only practical thing to do. PRS cannot collect the data themselves: they have to rely on the licencees otherwise the overheads would be unbelieveable.
Major radio stations, TV companies, major concert halls and the like are required to report every single item they play. They have enough resources that its not an unreasonable overhead. I think small radio stations, big clubs and the like are required to produce sample data. I think quite a lot of the sampling at big venues is done with people sent to the venues. Small venues and licencees aren't required to report at all. For why see below.
So the PRS end up with a pretty big database of what's being played out there. Everytime your stuff is *recorded* as having been played you get a cut of the income in proportion, less the management overhead, which ranges between 12 and 25% for different income sources. PRS is a "not for profit" so there are no shareholders getting a cut.
At the top end the cut you get is going to be pretty representative, but unfortunately at the bottom of the scale it runs into statsitical problems... If your tune is played once and it hits a sample venue or day then you get paid and paid more than one play strictly warrants, if on the other hand you miss a sample with your one play you don't get paid at all.
There's obviously a constant juggling match between accuracy and overheads... The more accurate the data gathering then greater the overheads in gathering the data are, and whilst the payment distribution is fairer the actual money the performers get is less.
All this is on the PRS website, but maybe takes a bit of reading, I suppose I've taken half an hour to research this comment.
Why small venues aren't required to report...
Consider, for instance, many years ago I used to work in a takeaway food shop where all the staff were major music fans and quite a number of us were semi pro musicians to a greater or lesser extent. We had a PRS license and we had something like a thousand tapes in the shop (we counted them one quiet evening when we couldn't decide what to put on next). Those might be tapes of albums, our own compilation tapes, even our own demo tapes. When you were really busy when a tape finished you'd just throw in the nearest one to have some noise... PRS could have handed us all the forms and order us to tell us exactly what we'd played and we'd never have bothered.. Well, maybe those of us with PRS membership might have been tempted to lie and say we'd played our own tapes all night and fuill in the forms like that...
So in many environments PRS could spend as much time as they like asking what's being played and they won't get an answer. Its hard enough to get places like shops to buy PRS licenses at all... I expect there's some dumb *****s out there who will say that if they aren't prepared to have a full time employee in every venue collecting all the data they shouldn't bother, but they won't have got this far down the essay anyway.