Many people who are in long term unemployment already feel that way. (I think that's my case.)
There is no political motivation to just take unemployed people and just create businesses and do something with them, so I think it's a problem of entrepreneurship. It should be a huge opportunity, but it's not getting done for a simple reason, people consider lazy people to be subhuman moocher and they don't want to deal with them. It is plain stigmatization. People pity the unemployed, but they don't want to help them eitherway.
The thing about the UBI, is that it simplifies the process of welfare, but it also stimulates consumption, which in turn boosts the economy.
Do you have any evidence for the existence of these lazy people, and in any significant number? The literature and actual experiments done with basic income shows that people are not lazy, but rather they lack opportunities, or a safety net for small risks, or any of a number of other things.
Basically, people who were working out of desperation worked less, otherwise people used the money to ensure food safety, invest in businesses or improving their lives.
I really don't think "lazy" is a valuable label. It tends to be applied when there are underlying causes for the supposed "laziness". When those causes are repaired the laziness tends to go away. For example: illness, precarity, hopelessness (as you mentioned), a lack of opportunities. I'd suggest doing away with the overly simplistic "lazy" and using more accurate words which express the underlying causes.
In theory, sure. But in reality, most jobs suck. Even if you are of that level, odds are the job you'll get is going to be emotionally or mentally draining, and at the end of the day, you'll really just want to relax.
Not everyone is smart enough to be productive in a competitive society.
The basic income is going to prevent larger potential problems with them, like crime or health costs or decreasing property values or other social expenses, beyond their immediate income expense.
These people already cost you money. The basic income is the option where you pay them little now so you don't have to pay a lot for them later.