This is demonstrably not true. I mean, it's tautological. We have the economic surplus to support the unemployed, yet we do not. Therefore, the problem is not the lack of economic surplus.
People have noted this apparent perversity for well over a century, but it seems unlikely to change anytime soon. So the question isn't whether transemployment is preferable to some lower-friction redistribution scheme, but whether transemployment is better than letting those same people starve, or die from opiate addition, or alcoholism, or diabetes, or any of the other methods of benign neglect by which society has found to execute the economically redundant.
Also, I'm not sure that "the entire purpose of work is to create value" really encompasses the role of "work" in American society. The creation of value is, to the worker, often a side-effect, since that value in the capitalist model generally accrues to someone else besides the worker. The purpose of work for most workers is to bring in wages, which are necessary for personal comfort, but more importantly (above a certain level) as chips in a zero-sum game of social hierarchy. Extracting value from labor is the province of the employer; extracting wages from time spent, regardless of value created, is the province of the worker. The capitalist market's labor economy is the resulting intersection.