It is an interesting subject. In my time as CNCC access officer no landowner I dealt with had any inclination to fill in potholes. They did not like untidy digs left in a dangerous state though. Keep them covered is good advice.
Generally landowners and farmers are against fencing off potholes. I did offer at one time to see if we could get fencing funded and done by volunteers to save the occasional sheep. They didn't want it even if it was free to them. The reason I was given is that any fenced off areas is then excluded from subsidy funding calculations. The larger potholes which were fenced a few years ago on Leck were done under a scheme. The purpose of them is to protect the rare flora, which grows on the exposed limestone, FROM the sheep.
Across the Dales, it appears to be acceptable to lose a few sheep down potholes.