Someone working an entry level fast food job earned vastly more than that per year.
Let's redo your math using realistic numbers and then we can see what's possible or not.
You have to, otherwise you assemble a perverse incentive to not be productive or work. We want less of that as it is, not more.
Working doesn't just mean "working for the man", it can be anything productive that results in income. Such as making and selling paintings, music, whatever.
However, there cannot be a reality where choosing to not work rewards you with as much or more than those who actually work. We also cannot have a system where people choose to peruse fruitless endeavors simply because they enjoy them, and then still get government payments. Yet, the system you propose will be just that - "I need it more because I'm poor - I'm poor because I choose not to work".
The money used to pay these people is complex, but it is not "free" and is largely supported by the working class. We cannot build incentives for the working class to stop working and subsist entirely off government payments (which come from the rest of the working class, leading to a downward spiral for any such program in terms of costs to the nation).
So realistically, the numbers for some sort of UBI are far, far greater than most people admit in these debates (as all-things government tend to be).
Additionally, if the tax equals the original labor, then there is now a negative incentive for businesses to adopt technology and replace employees as well. Employees are more flexible than a robot, for instance, so if costs are equal the human is the better value from the perspective of most businesses (some excluded such as maybe manufacturing).
Your system falls apart if more and more people decide not doing anything at all is a worthy trade off for a reduction in annual salary.
But that's not the scenario that is being entertained here.
We're talking about a hypothetical future world in which robots with AGI are capable of performing basic labor. Incentivize a human all you want, they will never be able to compete in a labor pool where their competition has no rights and will work 24/7.
That being said, a handout is not the best way to use that money anyway. What it should be used for are stronger safety nets and public services, along the lines of what already exists in western nations.
Lets say that robots cut US 'labor' costs in half -- from about 10 trillion to 5 trillion. Add in a 5 trillion dollar tax on robot labor and you've got about 14,700 per capita to spend. And costs for businesses don't change.