If an employer is going to take 40 hours of time out of an employee's week, then that employer needs to make that time worth their effort. A job taking up half of the employees daytime availability should pay a wage that is conducive to maintaining that employees effort.
That being said, an employer should reserve the right to fire any employee who has proven themself to be a burden on the company, and should not face lawsuits for firing an employee that refuses to put an effort into the job. If they're being paid to do a job, they'd best do it. Termination should not require 50 examples of tardiness to make ultra sure the gay black woman wont decry discrimination.
This would not have the same effect a minimum wage hike would have like what happened with McDonalds, where all real workers and slackers got a $15/hr pay, but rather gives them the opportunity to reward employees who make an effort, as well as give an employer the opportunity to staff their business with minimum wage employees. If you want minimal work effort, you can pay for minimal work. If you want employees who will have no financial reason to slack off and every reason to do their job, then you can present you're dedicated part timers with the opportunity to make a livable wage by going full time. This would deter slackers from full time positions as it would be mush easier to term them, and reward full timers with a wage that made their jobs valuable. Retention of employees would be optimized for valued efficient workers and reduce the number of gibmedats in those full time positions.
This would also allow for management positions to be optimized towards the part timers rather than towards full timers who have proven their value to the company, and will have little desire to slack off in the position. This way management can focus on cracking the whip in the problem areas.
Having worked multiple jobs in my past, many coworkers had refused full time positions since the pay never added up to the positions. Some ultimately took the positions who were fantastic part timers, but would last maybe a year before quitting since the time and the pay never added up for what they needed. Others would take on another job and work 60+ hours a week and couldn't enjoy life and ultimately break under the workload. Their full time job effort would frequently suffer and the write ups would soon follow since they were working themselves to exhaustion.
I've also seen full timers slack off as they accrued a corporate equivalent of tenure, which made it difficult for the company to fire burdensome full timers since they knew who in HR to call and complain about management who tried to get the slacker to do their job. This would effectively deter management from holding full timers accountable to the position they were working in.