As the law currently stands naive anglers new to the sport could quite easily fall fowl of the law even when they have paid to fish at a specific venue.
In addition the rod licence might actually be costing money by discouraging new people to become keen anglers. For example, I am a fairly casual angler but I probably spend in the region of £150 per annum on fishing tackle and paraphernalia – or something like £25 VAT plus perhaps £50 tax revenue from the £200 in fees I pay to angling clubs. So eliminating a single angler due to a £27 rod licence might actually cost the government £75 per year in tax revenue.
In conclusion, fishing is an excellent pasttime which anyone can enjoy – I don't think we should create unnecessary red tape around a sport which helps people to relax and have fun.