...because it's not legally saleable to you.
1 The V5 log-book is the sellers' PROOF OF OWNERSHIP of their vehicle.
2 If the seller doesn't have one, they have no proof that they own the vehicle.
3 Q. What's the worst that could happen to you?
A. Maybe they don't own the car, because it's stolen! This happened a few years ago to a good friend of mine, who handed over £3,500 for a VW Golf GTi, and was pulled by the police three days into his ownership... The car was returned to the legal owner, and he never got a penny back.
A. Maybe they don't LEGALLY own the car, because it still has hire-purchase payments outstanding from the used-car dealer it was bought from, maybe on five-year terms... You can buy the car, if you don't mind a finance company sending the big, bad repo-man for it at 3a.m. Or the police pulling you over, and arresting you for receiving stolen goods...
4 If the seller doesn't have the V5, maybe they have honestly lost it, in which case they must realise that the best way forward, for all concerned, is for them to obtain a replacement from the DVLA, who will still be listing them as the registered keeper. This will only take a few working days - if they have nothing to hide, what is the rush? If this is chargeable, isn't it only fair that THE SELLER pay for their failure to keep the V5? I have - RECENTLY - seen listings stating that "the V5 can be obtained from the DVLA for £19, so remember to budget for this in your bid"... How arrogant is that! The 'seller', who is on very thin ice, legally, for trying to sell a vehicle they DO NOT HAVE CLEAR TITLE TO, wants YOU to pay for, and deal with, the DVLA, who may well be unsympathetic to your case - particularly as the DVLA have been advising, with every road tax reminder they have sent out for the past couple of years, that YOU SHOULD NOT BUY A CAR IF THE V5 IS NOT PRESENT.
5 It is now the SELLERS' responsibility to complete and return the V5 to the DVLA. If the seller doesn't have the V5, how can YOU inform the DVLA? Well, if you really must buy the car, if it's only an old banger, sorry, 'classic', that you want the glass out of, that you aren't attempting to return to use on the road, you could just keep quiet, take the car, strip it of the parts you want, throw the rest away, and hope for the best. If you want to use the car again, you can check with the seller that they will happily give you a fully-itemised reciept admitting how long they have owned the car for... It's far easier for the seller to just obtain a replacement V5 from the DVLA.
6 Finally, as a seller, you shouldn't think of letting a car go, without completing the V5, as this is your means of severing your association with it... If that car is involved in an accident, maybe a hit-and-run, who will the police come after? You! "Oh, so you sold it did you, sir?" I bet they've never heard that one before... What about recieving a load of parking tickets? Or baliffs attempting to serve a demand for mounting unpaid fines, from the car being parked on private land, then clamped, towed-away, and kept in a compound. All this has happened before, and will happen again.
The V5 is there for a reason. It protects both buyer and seller. If the seller doesn't have one, don't consider the vehicle as theirs, and certainly not as yours! Without proper regulation, we have the thin end of the Wedge of Anarchy.