(Unfortunately no primary sources are cited for that claim, which is pretty common for articles on the topic.)
A solution with similar benefits but minimal perverse incentives is the Basic Job - if you can't find a job the government will give you an unpleasant one at below minimum wage.
Basic Job is horrible idea. It means hiring someone in made-up job. You take all the time that this person could spend with his/her family/children or on self-improvement or looking for a worthwhile thing to do, waste some of your resources that are required to set up this made-up job and pay so little money that the person will struggle to support himself/herself.
Communist states had basic jobs. I lived in one, it wasn't pretty. People got bored and lazy at the job, drank a lot of booze at work to kill the boredom and not care about what they did at all because that they knew they'll get their sh*t-money anyways.
Nowadays part of civil service office workers in my country fit the description of Basic Job. They sit 7-8 hour pushing unnecessary papers for near minimum wage. They are wasting their lives to prove that they deserve a handout. It's most often women that can suffer low pay and toxic work environment. Government could reduce much waste if it just sent them home with the same pay so they can take care of their children better instead.
They aren't made-up jobs. They are simply jobs with value lower than minimum wage.
In the US, we are often told about our "crumbling infrastructure". Roads have potholes. It's not hard to find parks which are not as well maintained as they could be. Government buildings are rarely spotlessly clean. If we are going to pay people who can't find a job in the private sector, why not have some of these problems fixed?
Similarly, many people complain that the cost of day care prevents productive women from working. If we are going to tax a productive businesswoman to pay for a basic job, why not at give her cheap day care (provided by low productivity people) in return?
The problem with Communist states is not the existence of the employer of last resort, but the lack of anything else.
Just give more money to you government and it will hire more people to do the jobs that currently it thinks it can do without. Like keeping government buildings spotless.
So the only thing you need to do to realize the idea of Basic Job as you see it is give more money to your government. Pay more taxes. Vote for people that want to raise taxes. Government will gladly use your money to hire people at minimum wage to do the jobs that have value lower than minimum wage. Or just move to Sweden.
Of course other people will say that government pays to much for cleaning parks and government buildings and filling in potholes. That it's not done as efficiently as it should be. And they will also be right. After all, why invest in labor saving technology such as cleaning machines if half of the point why this cleaning job exists is to have an excuse to give money to the person that can't find a job that has value higher than minimum wage.
So you don't want to give money to the people who currently are not gettinga any? You just want to discurage people who are getting money by ordering them to do some work?
Where do you get money to pay people to organize the job and supervise that it's actually done? How do you treat people who don't do the job right? Do you deny them the money and the job? Do you put them in jail? Communist states did that.
What do you plan to do about people who won't take the money if they have to lose third of their time for it?
Do you give those people money/food/shelter for free or do you let them starve or freeze?
I believe your idea is incredibly complicated in detail. I like the idea of basic income because there's so little that can go wrong. The only proble I see is that rent could just go up and suck almost all basic income into pockets of property owners.
First, we already have such 'free income' in forms of various welfare programs and SSDI. This creates a whole number of issues, however.
The problem to the perverse incentive problem, however, is not to remove the income when they get another source of income (as effectively it ammounts to a 100% tax!) -- while this may prove difficult to pass through any legislature, another approach could be to frame it as a progressive negative income tax.
That said, this is a different problem than homelessness: the two causes are usually extremely expensive housing and mental illness rather than lack of work. Mental illness means the jobs aren't stable, but extremely expensive housing means that even if they have a job, they won't be able to have a normal home: I've noticed this pattern a lot in San Jose, there are many cases of people living in their cars, used RVs, using work/gym to shower, and so on... They actually have jobs but are unable to go through a credit check and come up with an initial deposit.
This kind of housing solves both problems: the mentally ill have a stable address which makes it easier to follow through with a treatment problem; those who don't earn enough to get a place, can stay long enough to be able to save more, get a better paying job, and/or find roommates.
Free income to those without jobs is often arranged as to create perverse incentives. Free income period doesn't provide much in the way of incentives at all. So no it doesn't.