I'm not supporting 4X4's and the like but, bridleways came about as thoroughfares for horses at a time before these 'green lanes' were used for recreation. At a time when horses were the main form of transport. They would have been churned up by the horses at certain times of year and I bet pedestrians complained about them as well.
I can't remember if it was Surrey or Sussex but I was with a sizable group of people walking along a bridle path, when we encountered two or three people on horses. They weren't happy to confront us and were vocal about it and we was weren't happy about them and the churned up lane.
Recreational use, has altered the status quo.