"f the publican believes that they took £1000 but the cashless provider claims they only took £900, how do you prove it?
With cash you do a recount of both ends - till roll and contents. Can't do that in a cashless system."
There's nothing to stop you having a till roll recording every transaction in a cashless system. You need that information for replenishing your stock and checking that some of that hasn't "wandered".
The cashless provider does NOT get to tell you how much you have sold. You keep your records, they keep theirs, and they are reconciled on a regular basis.