Footpath use changes over the years of course. Some fall out of use, while others become bridleways or roads. I don't see why some footpaths cannot be used for cycling. Around here there are plenty that are as wide as a lane, and make useful alternatives to busy and unpleasant roads. There are others of course which are completely unsuitable for cycling where it would be rude and inconsiderate to do so.
Here's a photo of one footpath ideal for cycling near me from JME's excellent cycling blog: Keep Pushing Those Pedals (I hope he won't mind me reproducing it here).
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Just saying, it's the law, in a blanket fasion ignores such local inconsistenices on the ground. Footpath use changes and laws should reflect that. As DM stated above, I'd also much rather see people arriving at nature reserves by bicycle than in Volvos, which is what they do around here! Wicken Fen, a famous nature reserve nearby has a national cycle route going right through the middle of it. It's brilliant. Perhaps we should close it and insist everyone comes by Volvo and the like instead! We'd need to double or triple the size of the car park, but it's only a SSSI so what the heck!
I cycle many footpaths similar to your photo on many I don't see any walkers, there is a lot of talk about how unhealthy people are and we all need more exercise, some of the less used footpath's should be opened up to cyclists so there is more options than road cycling which does put people off and many footpath's connect existing bridleways this would open greater route choice for people to match their ride to their fitness, I don't think it will happen, there has been several petitions to get the paths open but no action, from the number of people I see riding them this seems to make little difference. I have no problem sharing the countryside with anybody, whether I am cycling, running, hiking, bird watching, or just relaxing having a picnic, but it seems not everybody shares my views.