Without a doubt, federal and state governments should use means testing to redistribute wealth to the poor. However, such testing should be high uniformed and feature slightly elevated requirements. The poor and even the rich take advantage of federal programs all the time, and the key to success involves eliminating these people from the programs.
Yes, there is a gap in the distribution of wealth, and its only growing larger and something needs to be done, when a middle class worker is paying more in taxes than large corporations who makes millions there is something wrong with that picture so any way to shorten the gap all for it.
Means testing means that poor people lose what benefits they have if they start to work, sometimes at such a rate that makes it a financial loss for them to work, but necessarily meaning that work is less valuable to them than to others. And means testing is difficult - people always find ways to cheat the system, and there are always some in need who get left out.
If some flat basic benefit were given to all - even though it would take a tax increase somewhere to support this - there would be no need for hordes of government workers to be paid to check what everybody was entitled to, and no risk of anybody cheating the system. Further, poor people could enter work with no fear of losing what benefit they had.