Let me try this another way, let's assume you owned a construction company
who needed unskilled labor for short periods of time. Your needs would
vary, from needing no unskilled labor to needing 50 short term unskilled
employees. Do you think society/government should mandate that you keep
these people on the payroll for the full 52 weeks and pay them a respectable
income, even if their services is not needed?

Of course not.



Society/government also mandates that we just increase the minimum wages so
that all an employees earn a living wage.
You build the rest of your argument around this false premise, so there is
little else to respond to. The government does not mandate that employers pay a
"living wage", or enough to meet all the expenses any family could run up by
having a dozen kids or living a lavish lifestyle. The purpose of a minimum wage
is to assign at least that much responsibility for the survival and support of
an employee, measured in dollars, to the employer rather than to the
taxpayer-funded social safety net.