If the trackbed is converted into a bridleway, it effectively removes the possibility of it ever becoming a railway again. Horses and trains don't mix. The upper dale is virtually all open access land anyway, apart from the valley bottom. With rising fuel costs and an uncertain world, private transport could eventually be a luxury only the few can afford. Surely we should be safeguarding potential railway routes for future generations?
Actually it preserves the route. Otherwise people tend to do stuff like building houses on it.
But that aside, the correct solution for public transport in Wensleydale, if the situation you describe arises, is to fully reinstate routes 156/157 (Northallerton-Bedale-Hawes-Garsdale) as an hourly electric bus service, not to reopen the railway for public transport. These routes (and what remains of them) were ironically created by...the Wensleydale Railway!
Even if cars were banned entirely, the Dale is too sparsely populated to justify more than that. You'd just see more cycling and e-bikes too.
Arguably, like Keswick, the cycle path will probably be of far greater value, as the road is horrible to cycle on, but it's just fine for running buses along, and they go closer to some of the settlements than the railway ever did.