If I was a fishery owner, I wouldn't want the additional hassle of having to challenge and check everyone entering my fishery. I would be running a business, not acting as a policeman.
If it was put into law, then that would be something they would then have to police, but whilst it is not an obligation, why should they enforce checks. Buying a ticket to fish is not like purchasing alcohol. Do you need to show a car salesman your driving license to buy a car? It's the same situation. If they start acting as an enforcer without the legal obligation to do so, there are unfortunately a minority who will start making threats.
The EA are a non-profit QUANGO, partly funded by DEFRA.