Or we could just let workers and employers sort it out.
In practice, "let workers and employers sort it out" means, "let employers dictate whatever terms they want." That's especially true in this case. If new technology lets them get more work out of fewer employees, then employers have all the leverage and workers have none. Cutting workers is what the employers want to do anyway. Workers are left desperate for work. They either accept whatever terms the employers dictate, or they starve.
You could have made the same argument against almost any worker protection: minimum wage, standard work hours, safe working conditions, etc. "Why would I (which really means society) get involved in you (meaning all workers) negotiating your wage, work hours, working conditions, etc.?" The answer is the same in each case: if society doesn't get involved and set rules, you end up with a really bad result where a few people profit and most people suffer. That's not hypothetical. Every worker protection that exists today only exists because in the past, employers abused their employees and laws were needed to end the abuse.
A "free" labor market without laws leads to a bad result. Laws improve the result. That's the simple reason for them.