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It would help keep people out of poverty and reduce poverty related costs.
People who aren't worth high wages will be far less able to find fulltime work.
If you were being paid under minimum wage for full time work, it would be illegal.
This would encourage businesses to make most positions part time and only retain a few token full time positions as part time has not been held to equal standards.
To some degree this wage should be supplemented by the government, to avoid causing unemployment
This would be a horribly impractical law. "Full time work" is arbitrary and there is no reason that people should have to work that long for a basic standard of living.
Improving education, the social safety net and business opportunities is a better bet.
Not everyone who wants to work needs a living wage. High schoolers living at home in the summer, Elderly supplementing Social Security, etc.