I do know gardeners who do unwalled raised beds, but when I tried it, it was a pain because the soil tended to wash off the top of the beds into the ditches so the beds tended to flatten out - this isn't a problem for ridge and furrow, because the ploughing automatically throws the soil into the middle. Also there was no weed barrier, which for small square or rectangular beds opens up a lot of space for weed invasion: again, less of an issue for a big strip bed.
It would do away with most of the problems of allotment management - if the whole length was ploughed yearly, then you wouldnt' have the problems that you get on many allotment sites where you have one plot that is neglected and affects everything else. The ploughing being done centrally would mean that people not able to dig would be able to garden a stretch. Any unused areas you could cheaply put down to green manure, or even just sprinkle on some flowering annuals, knowing that they would get turned in and not end up running all to brambles or nettles. It would be a good community thing, and say you had a ridge and furrow running behind a street of houses, everyone would have access to vegetable gardening without having to maintain a huge garden. I suppose the big problem would be: who gets the ox?!