The difference is you now loose the current month, that has already been paid for.
1) Person A is selling a car and it is currently taxed to the end of the month.
2) Person B is buying the car.
'A' can't claim the partial month back.
But the car remains taxed to the end of the month.
Person 'B', once sorting insurance out, could happily drive off, and worry about ordering a new tax disk before the end of the month.
'A' still can't claim back, as it's a partial month, so no change there.
But now the current months tax is not transferred to the new owner, so is effectively scrapped.
This means 'B' now has an untaxed car, despite 'A' already paying for this month.
So 'B' now has to re-tax the car immediately to be legal.
Therefore the DVLA get paid twice now for any month where the car changes ownership.
While I can understand to some extent not transferring the full month over, (as the tax payment would still be in other old owners name, not the new), they should keep the partial month on record, to give the new owner time to sort things out!