I'm not sure some job safety issues aren't a reasonable use of government.
Suppose I work in a place I believe is safe, but the employer knows it is not, and doesn't tell me. Unless I have specialized knowledge, I won't know it isn't safe. What is my recourse if I am harmed?
Government's role in this case may be the court system and punitive damages, but there needs to be some check on behavior that might not be provided by the free market.
My classic example of a free market "gap" is the use of rivers. If I'm upstream from you, it might make perfect economic sense for me to to use the river for my waste, disregarding that I'm spoiling the drinking water for thousands of people downstream. There must be some recourse for these kinds of gaps.
Now, if I knowingly and willingly take a job, and I understand the dangers, there should be no recourse.
I would, however, like to see certain regulatory practices taken over by private companies. For instance, the FDA. A private regulatory agency, or multiple agencies, could inspect food and give it a seal. If the food didn't have that seal, perhaps there would be a market consequence.
As to job safety- currently if the worker is injured the Worker's Comp carrier is going to have to pay benefits. During their investigation they generally will determine whey the injury occurred. If it is due to a problem with the premises or a work process, they will require the employer to fix it. If the employer refuses they will likely lose their insurance with that company and it will be tough to get another company to insure them. If injuries continue, rates will increase. Of course state government requires employers to carry WC insurance.
If we went back and dropped the mandatory nature of WC, we would return to the situation where employees would have to sue the employers. That is a slow and cumbersome prospect. It is also costly to all parties except the plaintiff attorneys.
Unfortunately I don't think we could ever get rid of all government (including courts) intrusion in to employment situations, as history has shown that employers are willing to treat people pretty badly including children to maximize their profits. It has also shown that a sufficient number of our fellow citizens would still be glad to buy their products for the cheaper price, knowing how the goods are produced.