Why completely revamp a program that works, when there is already one that provides what you say will cure simple poverty? Welfare already provides money to live on and job training.
That is just You claiming a complete revamping. Nothing much would change. Unemployed persons would still apply for UC like usual. And, any "revamping" would mean employers don't have to keep track of unemployment benefits issues and become simpler for employers. UC is a State issue not an employer issue. So, if by revamping, you mean simplification, then yes it would be a revamping.
The point about welfare and our war on poverty is that it is less cost effective. Welfare spending only generates a multiplier of around point eight (.8). while UC has been measured with a multiplier of two. Considering that the cost of our war on poverty has already been around twenty-two trillion dollars it should be, a no brainer, to resort to a more cost effective method of solving simple poverty.
Consider that a multiplier of .8 times the cost of our war on poverty to date, around 22 trillion only generates around 17.6 trillion in economic activity while UC would have generated 44 trillion in economic activity with a multiplier of 2 with that same amount spent.
Only right wingers complain about a rising tide lifting all boats.