Precisely. This is an easy cost the railway could cut - cash processing is hugely, hugely time consuming and expensive, and also renders the guards more liable to assault by someone looking to steal the not considerable sum they often have on their person.
I'd love to see what the stats would be on savings (including from evasion reduction if PFs could basically become absolute) were a franchise like Northern to abolish cash payment (a) at non-staffed stations, or (b) entirely, and what that money could be spent on instead in terms of the service.
An option (c) could be added of what it would cost to offer to those wanting it a Northern branded prepayment debit card without any fees. Those wanting to pay cash per journey could simply go to a newsagent or other PayPoint/PayZone and load it with the fare before going to the TVM with it. There are people who use Oyster in that way. People with that kind of "closed horizons" are not typically going to be tearing all over the network, they will be making known local journeys with a mostly known fare.
On numbers I can make an educated observation. From what I understand there are something like 600 card only ticket machines on the Northern network, and a card only machine is roughly £10,000 cheaper to buy than a cash and card one. Therefore, you're looking at a something like £6 million saving by installing card only machines, and implementing a scheme like "Promise to Pay". And that's before you get on to the increased operational costs of collecting cash and dealing with the inevitable attempts (successful or otherwise) to steal that cash, which invariably result in costly damage.
So, based on the pure economics, I can make my own "armchair expert" observation that there must be an awful lot of other helpful things Northern could spend £6 million of capital expenditure on... Answers on a postcard please
As to Promise to Pay itself, I suspect this was a well-intended effort to accommodate users wishing to pay with cash while freeing that £6 million to spend on something else (or not take as subsidy from the tax payer). I suspect there are many opinions here on how well Promise to Pay has been implemented operationally (I've plenty of my own), the fundamental concept seems sound to me. Specifically, giving the honest passenger a means of proving where and when they boarded, and giving the TOC a means of challenging the dishonest passenger. It's far from perfect, but it's a start. A lot of the challenges seem to be in the operational implementation of the associated revenue protection "catching" people who fully intended to pay and therefore didn't really need "catching", rather giving their opportunity to pay the best value fare.