It's far less economically distorting to top up a family's income with an EITC than by mandating higher wages. For one thing, it avoids giving employers incentive to cut back on labor costs.
Lack of demand, on the other hand...
Yes capitalism is amoral so people will certainly be willing to pay to increase salary, but they are also willing to buy machines, outsource work, make customers do more and other things that reduce the need for employees.
Where do you think the money for EITC/WTC comes from?