If you plan would end poverty, then the welfare/food stamp/Section 8 housing systems would have solved it. Changing the source of the money does nothing.
That is Your unsupported assumption. Means testing cannot solve simple poverty in a market friendly manner by definition.
And, means testing is being misused in our alleged war on poverty. Means testing should be for those for whom solving for a simple poverty of capital under our form of Capitalism may not be enough. Means testing should be used to generate metadata in order to concentrate wealth to solve more complicated issues that prevent persons from leading more productive lives in our market based economy.
Means testing is an attempt to stop people from drawing a check if they do not need it to get by. That is all. Without means testing, someone with $100k in the bank could draw welfare. Or someone who has a spouse with a good job, owns their home ect, could draw a check from the tax payers. If UC is ever changed into what you want, there
will be a means test. I assure you of that.
If the only qualification for UC is that the person does not have a job, every retiree in the US would be applying for it, despite having a pension or 401k.