Of course you ignore the comment that was in reply to...

I reported his too, don't worry.

Uh, its free stuff.

Firstly, read past the first sentence. There's a difference between quantity demanded and demand itself. If supply increases (say though making programs more appealing), then the quantity demanded increases; the demand itself does not increase. This doesn't change your perception of what's happening; more people will enter the program, but your terminology is wrong.

UI is a perfect example. Why in the hell would someone take a minimum wage job to come off UI when the job pays not even 10% more than UI?

People may still pursue a part-time job to greater the quality of their leisure. Yes, they will work less, but it's not a guarantee that they will stop working entirely. See this example. Providing a cash transfer such as UI would shift the budget line but still remain tangent with the indifference curve. The curve itself exemplifies diminishing returns on leisure with reduced disposable income and diminishing returns on disposable income (acquired through more work) with reduced leisure time. I agree we'd see people working less, but is this an improvement for society as a whole? Does the social welfare match the costs? I'm not sure.

Have you ever used these programs? Do you live a bubble where you don't know anyone that has?

Do I need to use these programs to understand how they work? Is it a necessity that I be poor to suggest we rework welfare?

And you can make claims about the EITC and NIT without a citation, but require one from me.

EITC works in a sort of opposite way to UI. Rather than a flat transfer that increases the budget line, it creates a kink that leads people to work more. Less formally, it subsidizes income, which leads people to pursue more. On the other hand, income tax itself is, obviously, a tax on income, therefore it reduces the incentive to pursue more of it; because income is linked to productivity, this may be considered distortionary.

Negative Income Tax is the opposite and may be considered distortionary as well. However, as a replacement to welfare, it may be an improvement. As you noted, welfare promotes more leisure while providing financial aid; NIT, by subsiding income, provides the very same financial aid without the flat cash transfer effect on the budget line. In effect, it creates an incentive to perform some amount of work to "earn" the welfare. This may lead to people working harder such as in this example that I drew up where NIT is provided after a minimum amount of work; here the amount of leisure people engage in goes from Q1 to Q2. It may also lead to people working less, empirically and theoretically. Additionally, it may simply be more efficient; for example, rather than taxing people and then giving them back welfare, it's easier to just tax people less in the first place. Here's some more information. A significant goal of both tax programs is to avoid the perverse incentives of an existing welfare system.