"Radical wealth redistribution from the needy to the rich is a far right idea, and that's what the negative income tax will boil down to in practice."
The term wealth redistribution is generally understood as wealth going from the rich to the poor and is a "left" idea[1]. And even it it is not, I cannot think of a (sane) negative income tax system that can be described as wealth going from the poor to the rich.
But you seem worried that a student is different from an elderly, and to give both negative income, the elderly will be worse off than in a system like today? All I can say is that nothing in what was described so far implies that. If you have special needs, you might be eligible to more negative income tax.
"there is not enough money to give every adult citizen the equivalent of social security"
Sure there is, because a 125[2] of the 240 have a job, those who earn little, might still get some money from tax, those who make medium pay a some tax, those who make a lot, pay a lot of tax. But it will imply more tax on the rich, both income and wealth. (Though nothing ridiculous.)
[1] https://en.wikipedia.org/wiki/Redistribution_of_income_and_w... first line "Redistribution of income and redistribution of wealth are a concept of socialism"
[2] https://www.statista.com/statistics/192361/unadjusted-monthl...
Why I am in favor (of UBI or NIT)? I cannot be described as a right wing, nor as rich. And any reduced administrative overhead would be nice, but not a goal per se.
But giving more money to those without a job, or low income jobs, has a few advantages:
1. economically speaking, money to those who have little represents more wealth, and will be spend in the market
2. a shrinking economy, means even more pressure on low incomes jobs, and less who have an income at all, that shrinks the market, and shrinks the economy, NIT can work like a buffer
3. low income people have no power on the labor market, a NIT or UBI gives them more power, with room to switch jobs, or go back and study
And a last one, but this depends a bit per country/state, people are usually eligible for benefits or not. Some of those tests are income earned, or money in the bank. So when people are almost eligible, but have too much money saved, they buy an expensive car and become eligible. Or you refuse a job, because the pay is not that much more then their benefits, but suddenly they have to work 40 hours a week and commute, etc.
Especially a NIT makes sure that these things are always a line, never yes/no. Made some money? You get to keep that, and most of your NIT benefits.