Your question seems to indicate a failure to understand what should be elementary capitalist principles as defined by Karl Marx. The thought experiment does not define ‘wage labor’.
In the situation you outline there would be no wage labor. UBI and public services would provide what is needed freeing individuals to make true personal choices. Marx recognized that it was the creation of an owning class that could control the state to ensure a working class with no other option to survive than to sell their time each day and lose control of that potion of their lives.
Here is a quote from Marx that should help: For the wage laborer, “The product of his activity, therefore, is not the aim of his activity.”