The problem is many farmers are fed up with the public leaving litter, letting their dogs roam free in livestock fields and leaving important gates open, often deviating from the actual footpath/bridleway, especially since 2020
I’m not convinced “responsible access” would make all that much difference. It’s not an automatic flood gate of everyone suddenly accessing everything everywhere. Most of the “nice bits” already have access routes, even away from high ground.
You might have a few problems on large private Capability Brown type estate grounds. But working farmland, is, by and large, pretty f***ing boring to your average Joe. A field edge in rural Northamptonshire is not going to attract a relentless stream of people. Although I’d guess without education there would bea an uptick of people wandering around at first.