I suppose there is an issue of calories here. If we wanted to eat potatoes all year we could provide most of our calorific needs but it wouldn't be a very exciting diet?
I'm also thinking about crops which crow well on allotments but don't transport very well (in supermarket lorries). These cash-crops would be beneficial to be grown in urban areas as you would get more money for them if you sold them locally.
While you could theoretically exist on only potatoes, it wouldn't be particularly healthy. You wouldn't get a good enough range of nutrients from a single veg.
On a lot of allotment sites, selling your produce isn't permitted. Historically the space was to enable you to grow what you need to eat, not to run a business. People generally trade or give away surpluses. There was a thread on this not too long ago.