So these 3 million unemployed people can be evenly spread out over the economy, sharing in 3/40ths of the jobs of doctors, nurses, machinists, programmers, cleaners, gardeners, engineers, chefs, management consultants, inbiss cook and street sweepers?

And this can happen with less than a few percent friction cost?

Explaining why this will fail, let alone describing how it did indeed fail where it was tried is econ 101 material. As someone else pointed out, look up Lump of Labour fallacy.