You may be misstating your point. UI was intended to ameliorate the effects of frictional unemployment. The premiums (in California) are paid by the employer. The difference between an at-will scheme, and welfare as we know it, is that an at-will unemployment compensation scheme is more market friendly. Our current welfare schemes are mired in "red-tape" and subject to much more fraud, waste, and abuse than the an at-will unemployment compensation scheme could ever be (since it is at-will).
In one sense, an at-will unemployment compensation scheme could be considered a minimum wage at which people can be paid to stay out of the labor market, and as simple to administer. I am of the opinion, that any public funding that benefits the markets, and our economy (thus, the populace) can be considered a form of providing for the general Welfare.
We already have welfare without responsibilities. It is called welfare as we currently know it. That scheme has not solved many of our socioeconomic problems, and is considered, by some, to not be conducive to the pursuit of higher education, art, or happiness.
An issue of homelessness due to lack of income could be addressed with a minimum wage subsidy based on at-will unemployment. Panhandling laws would have a more ethical, legal, and moral standing, if an indigent person could simply apply for at-will unemployment compensation. How does our current system solve for that?
Why do you advocate third world economics when we have a first world economy? What recourse does a person have in such an economy when there is no work available due to market inefficiencies that lead to frictional unemployment? Are you implying that the US (and its populace) was better off as a third world country during the industrial revolution?
An at-will unemployment scheme would also benefit the labor market and our economy by subsidizing less efficient labor market participants to stay out of the market for labor. With at-will unemployment compensation available, employers would be freer to exercise their Ninth Amendment right to create private social contracts that may result in employment, in manners more conducive to their private profit motive. How does welfare, as we know it, accomplish these goals in a manner consistent with out Bill of Rights?
I am of the opinion, that any self-respecting first world economy can afford to subsidize people to not provide labor input to the economy; in much the same way as corporate welfare subsidizes agribusiness to not produce commodities for the market. How does our current system provide for an income to people on leaves of absence?
The main difference between a hypothetical at-will unemployment compensation system, and the command economics of the former Soviet model you mentioned, is that an at-will unemployment compensation scheme is market friendly. In other words, market principles still apply. Employers will benefit by having more motivated and productive employees because anyone who would prefer being a couch potato could claim at-will unemployment.
With lower barriers to entry, the private sector could provide value added products to any guaranteed public sector unemployment compensation. How does our current system enable the private sector to create new and improved financial products for US consumers?
From another perspective, do you think that ancient Athens would be better or worse off, if they had simply paid Socrates a minimum wage based on at-will unemployment compensation?

