The other thing about saving is that if you can depend on UBI, and it's enough to live on, then that takes the pressure off of individuals saving for retirement. Right now the amount of money people have to save for retirement in the U.S. is actually a problem, because there's no safe place to put that much money. And so we wind up with things like private equity and various other forms of securitization a specific group of which led to the 2008 crisis.
All of these securities are just ways of storing value, but you can't actually store value—value is work. "Stored value" is an obligation that someone else will have to work to pay back: I use my wealth to pay you money to do the work that I need done.
So public support for people who need it is actually the same thing as living off savings, except that living off savings is individual, and public support is collective. So public support can take advantage of the law of averages, and private savings can't. Which massively increases the amount you have to save as an individual to be sure you'll be okay in retirement.
And this motivates wealth inequality, which makes things worse and worse for the people who are creating the value you as a person with a decent amount of retirement savings need done. We've already had people saying "no more taxes" because they don't want to work to pay for other peoples' retirements. This is the same thing, and at some point it either turns into runaway inflation, which means your savings loses its value, or else it turns into regime change, which means who knows what? Right now, it means that a bunch of elected people are just raking in money through fraud, which isn't likely to end well for the rest of us.
It's weird how people think of socialism as being somehow expensive in comparison.