It's often financially impossible for farmers to divert and fence footpaths. Firstly, fencing and it's upkeep is extraordinarily expensive. Secondly, herds are moved throughout farmer's land, to provide a continued supply of grass for as long as possible through the year. Therefore they'd have to fence every field the path encroaches on. Thirdly, planners often refuse the farmer's request to reroute a footpath to a route with less impact on their land. Rerouting would often also mean the installation of access points such as stiles, to prevent gates being left open.
I know of too many farmers who have not just sheep but also cattle attacked by loose dogs. When you enter a field with previously disinterested cattle, you cannot pressume they'll be disinterested or friendly every time. Once animals have felt threatened by humans or their pets, they're far more likely to become dangerous the next time their field is entered.