Any inefficient system can always be improved.
The system you are fond of retaining, already has sufficient anecdotal evidence as an obsolete economic model; and is still employed by most of the third world. How much crime would there be a private profit motive for; if anyone can obtain a subsidy, at minimum cost to the taxpayer?
What subjective value system allows you to place a higher value on poverty, than on more efficient markets that can improve the standard of living of all market participants?
Is it less holy and moral to pay people to be less exploited in the market for labor? In other words, no one will be able to claim they are being exploited by being paid to not provide traditional labor input to the economy. This type of consideration could be done for the public good.
How does your scenario ameliorate the effects of frictional unemployment on poverty?
An at-will unemployment scheme can eliminate "official" poverty at minimum cost, and could be considered a minimum wage at which the public sector will subsidize people to not work.
In this same manner, we could have zero "official" unemployment in the US market for labor by providing public sector competition for labor market participants.