How many staff would be required to check every ticket on a train between stops? On a busy train with eight carriages (average 70-80 people in each), if I have no hold-ups I can check a full carriage in about 8-10 minutes, quicker if all season tickets, slower if weekend leisure travellers. On my line most stops are 15 minutes apart, a few 25. If I have to actually stop and sell tickets, that gets slower again. And don't forget, my primary role is NOT to check and sell tickets.
As I said in other posts, barriers will stop the large number of "pay when challenged" passengers, which will free my time up from selling tickets to them. On-train checks are necessary as well, but they are much more effective if passengers boarding have some sort of ticket in the first place, as when forced to, most people will buy the correct ticket.
I've often pointed out the ticket sales for Grangetown station in Cardiff, the closest unbarriered station to Cardiff Central. Ticket sales to and from Grangetown dropped by over 500k a year after ATW barriered the main stations in South Wales. Passengers still turn up at barriers in Cardiff asking for a ticket from Grangetown, they have very often come from another unbarriered station much further away (Stapleton Road in one case a week ago).
Nothing works on it's own, Revenue Protection is a complex task, and requires a multi-prong approach. Barriers are a simple and proven deterrent, but sometimes are a victim of their own success as after they are in operation for a while, word gets around, the majority of passengers buy tickets, fewer passengers purchase tickets at excess fares windows, and some bean-counter decides there is no need to employ barrier staff as they are not taking revenue.
Working any peak-time train from Paddington, and/or weekend train, if a barriered platform, pretty much everybody will have a ticket. If an unbarriered platform, I'll expect to sell anything up to a dozen, in the two or at most three STD class carriages I'll get done before Reading. When asked, they will invariably have a story about running for the train - some of them I will have clocked on-board 20 minutes before departure. Some of them will be violent when asked to buy a ticket.
Barriers are a big, big deterrent to ticketless travel, in my opinion the single biggest one. Checking tickets is the biggest cause of conflict and assaults to on-train staff (lone workers). Anything that reduces that risk to staff should be increased, not removed.