At that point, the state (who is ultimately paying for most of this) would be competing unfairly with private companies (in particular, it would not be paying minimum wage). This is probably not a good idea.
In Ireland we have a scheme where an unemployed person can get an extra 50 euro a week on their unemployment benefit, in return for which they do an internship for a private company, which must at least in principle be training-oriented. In practice, this can cause a problem where these 'internships' displace the need to create real jobs.
The UK has a nastier version of this: you can be compelled to do unpaid work or lose your unemployment benefit. Some of this is displacing real jobs in the low-paid retail sector. Some of it results in people standing around in hi-viz jackets doing nothing for 35 hours a week. https://welfaretales.wordpress.com/2015/05/15/workfare-force...
The (rather idealised sounding, by the NYT's description) European version is about keeping people engaged with society by giving them things that feel like work so they have colleagues, a familiarity with working practices, and a feeling of usefulness.
The British version seems to regard sitting at home while unemployed as an outrageous privilege; drudgery must be imposed on those people otherwise they're better off than the 'hardworking' people who must suffer commuting and not seeing their family. A previous version was declared illegal, so the government enacted "emergency" legislation to retroactively legalise it. http://www.politics.co.uk/news/2013/03/19/ids-emergency-jobs...
Yep, Workfare is definitely far worse than Jobbridge (the Irish scheme); in particular Jobbridge is not mandatory (or even particularly common) and the internship has to provide useful experience and training (though there has been abuse of this; a major supermarket chain was advertising shelf-stacking jobs as Jobbridge internships for a while before getting caught).
It's a free lunch for all is it? Someone pays (if not the descendants yet to be conceived who will be making interest payments on current debts) so it's certainly drudgery on the folk who have to pay for those sitting at home.
I suppose that's how you keep the chain of economic coercion through threat of starvation going.
"We are giving you this free lunch, because we're uncomfortable with people starving to death in a first world country, but in order to maintain the strict ranking that citizens are only allowed happiness in proportion to their income, we're going to inflict useless activity on you. Don't have a nice day or it'll come out of your benefits."
(Current debt is being issued at 0.5% interest rates, a historic low)
Though you are correct that interest rates are very low, I believe it is disingenuous to quote the rate of a gilt with a maturity under 10 years. (You have mentioned the 2-year gilt.)
This system also likely works without making changes to wage laws etc, and makes clear that it is temporary and to help people get a job and not a source of cheap labor (which quickly would take over "real", normally paid jobs, which would mean more people are unemployed, ...)
You could do things that are not in competition with any company (or in minimal competition). For example visiting and having a chat with lonely elderly.
In Ireland we have a scheme where an unemployed person can get an extra 50 euro a week on their unemployment benefit, in return for which they do an internship for a private company, which must at least in principle be training-oriented. In practice, this can cause a problem where these 'internships' displace the need to create real jobs.