Which is, practically speaking, treating it as a criminal offence. Under the current system, it's largely treated like a commercial exercise, carried out by commercial staff from the TOCs.It's not so much about criminality, it's more around fining people and using the courts, if I was found with no ticket a fine is a bit like the fine for not using a seat belt in a car!
There's no doubt in my mind that doing so would massively reduce the level of fare evasion. But the public relations impact of having a 'police officer' check tickets might very well put people off of rail travel. It would be possible to have virtually 100% effective revenue protection (stadium-style turnstiles at every platform entrance and exit, for example) but doing so would cost so much that the railways are financially better off tolerating a small level of fare evasion.
What doesn't help is complex fare structures and ticketing systems where someone with no intent to evade a fare can be easily caught out, and where revenue protection staff can easily believe that someone with a valid ticket is evading the correct fare. Using BTP for revenue protection would make these problems far, far worse.