What you are describing here is essentially the English Poor Law version 2.0.
The system is widely regarded to be both somwhat cruel, and counterproductive to it's intended goal.
Yes, your model have a few differences from the workhouses of the 19'th century (mainly a bigger focus on education (the British used to believe in the ennobling qualities of hard labor, which meant the institutions were essentially slave labor camps) as well as the neat flourish of allowing inmates to engage in some heavily regulated forms of commerce), but in it's essential qualities it is the same system.
1. It proscribes that dependents upon the state's welfare be kept in institutions, seperate from the rest of the populace, and lose many of their civil liberties.
2. It assumes that unemployment is a result of vice. If a human is virtuous there will always be gainful employment.
1 is dangerous for a host of reasons, 2 is just plain wrong.
Civil liberties is more than just nice things to enjoy. They are also a safeguard against tyranny and exploitation. We can flee an abusive employer (or relationship). We can call out when someone does us wrong.
In your re-education camps the inmates are at the mercy of whoever runs the camps. The guardians already have authority to limit use of media in the name of combating "vice". What is to prevent them from abusing those powers to shut down dissent within the camps. What kind of mechanism would be in place to prevent a Magdalene Asylum scandal or something similar.
Putting people in camps is also a great way of stigmatizing people and marginalizing them socially. They lose touch with their outside network (that might lead to jobs) and gain a new, but much less useful "network" of campmates (much like a prison sentence can often make a man more criminal). Hell, employers might even discriminate against former inmates, if the populace at large buys into the whole "vice" theory of unemployment.
And then there is the issue with structural unemployment. The model assumes that the able and willing will always be able to support themselves with gainful employment. Is this really true? What are you going to do with a laid off steel mill worker when all new jobs are in the IT sector? What about about a construction worker after a building boom went bust? Are they to be incarcerated due to their rotten luck? Or do the "virtuous" just magically gain skills in whatever field the market demands? We live in a world where the demand of unskilled labor is constantly shrinking. We only need that many street sweepers or McDonalds clerks (unless the Gov't is willing to fund all kinds of "make work schemes" in the name of ensuring full employment). What about economic recessions/depressions, or lopsided trade balances like the game China is playing with the US in order to ensure (near)full employment in their own yard?
