Why should it hinder them in adapting to supply/demand? I don't see it adding any friction there.
They would have to look for shitty jobs that nobody wants them to do in order to get some money for living
We have that already. 2 or 3 shitjobs even.
The "absent workers" would be exactly what the name suggests: absent. Not working for the company, just being on their payroll. In simple terms, companies would pay for welfare directly, without the need for the state as middle man.
Firms should be able to focus on serving their customers and forget everything else. In this model the state is forcing them to do stuff that's not their specialty. They need to spend time, money and resources to deal with problems that have nothing to do with goods or services that they are offering to markets.
The state has to be the middle man. It's much more efficient than forcing firms to be middle men. This is about specialization: there should be only one institution that handles the whole social security system. It will offer same services equally for everybody so nobody is discriminated. If firms have to handle social security, the quality will be highly variable. Firms might have cash problems and social security payments are delayed (and poor people can't do anything about it) or firms can go bankrupt (and poor people have to find another ones to give them money).
It's much more fairer for everybody if firms are not forced to take care of things that they don't want to do and those who really need social security don't have to expose themselves to unnecessary risks.
Right now companies have a lot more work to care about taxes and benefits for all their employees. I'd expect less overhead for them.
I see the issues for poor people you mentioned, but I don't think that couldn't be solved easily either. The state could still jump in when problems appear. When the rates are set accordingly, it can be made easy for anyone looking for a position to get it (in return more companies would struggle to meet the conditions, so this has to be weighted very carefully).