Giving everyone a little backup makes for a better society where people can take the risks they should take.
x-m(x-c)=x-mx+m*c
Of course, that gets more complicated when it isn't a flat tax, but I would think that for those in the lowest tax bracket, it would be equivalent, because within that bracket it would be flat?
I'd be arguing from the opposite side, where you both get the ~$1200 in universal income if that is a normal pension amount, and then I'd expect the average HN reader to end up paying a little more in additional taxes than they get in income under a universal income plan. But over time, I think it will raise all ships.
There are many ways to implement that, but I think universal income has a better opportunity to remain intact and increasing once pushed through. Plans that try to achieve fairness through more complex benefits and scales tend to end up in tatters because they offer opponents a lot of surface area and ways to implement a thousand cuts where few people feel a connection to each individual part.
many vulnerable people don't claim even if they know they qualify because the whole process is demeaning. sometimes when you have lost everything, you desperately hold onto your dignity, even if that isn't profit-maximising. real people (as opposed to idealised economic agents) are like that.
many vulnerable people can't claim because they slip through the cracks. the process of verification can be intense, especially as the public demand absolutely no benefit cheats meaning everyone is treated as a fraudulent with a lack of empathy or compassion.
many vulnerable people have no incentive to save money (since that might disqualify them from receiving benefits in the future). this is similar to what happens with company budgets. you need to spend all that money or you won't get it next year when you might actually need it.
tl;dr its complicated. the end result depends on a ton of externalities.