What's wrong with requiring people receiving public funds to work for the public?
Well (he says nervously looking over his shoulder in case an economist is listening) there might (or might not) be a few things wrong with it.

Basically you are saying the government will guarantee a job to anyone who wants it. That seems to be what the TVA did. We tried to manage our economy at full employment between 1945 and 1979, and in a sense the government did guarantee jobs (by nationalising failing companies), and it was a disaster. Now, I don't know enough economics to know if it HAS to be a disaster, or if it was just badly done (the nationalisation route removed much incentive for companies not to fail which would not have to be the case if the government simply employed the unemployed directly, so I guess you wouldn't repeat that mistake, but the effect on wage inflation of full employment seems fairly unavoidable).

Also you do need a lot of surplus jobs that aren't being done at all. Sounds like the TVA did have a lot of those jobs but today it might be more difficult.

Finally it might be better for them to be in training rather than working. and some might not be able to work due to disability or caring responsibilities, though I would guess you didn't mean to include those.

All in all I'm not sure about workfare. I think its better to pitch benefits at a level where the moral hazard of chosing a life on benefits is low (which to be fair, it is in the UK, really no one is living the life of Riley on handouts whatever the Daily Mail may think) coupled with good training and education opportunities and more childcare places.