It's not basic supply and demand--indeed, most economists are pro immigration. Bryan Caplan went as far as advocating for open border (admittedly he's more libertarian than most).
Labor market is complicated because jobs are not a finite pool that people compete over. New workers are also new consumers, who create new jobs as well. If more workers are always bad for other workers, declining birth rate (ie fewer future workers) would be a good thing.
Profit margin is the wrong metric in this debate. The person you are replying to is saying that the insurance companies as a whole is a waste, including all the salaries paid to their employees.
Labor market is complicated because jobs are not a finite pool that people compete over. New workers are also new consumers, who create new jobs as well. If more workers are always bad for other workers, declining birth rate (ie fewer future workers) would be a good thing.