> Companies couldn't offer more money in a tight labor market
It was illegal for them to offer more money - Roosevelt instituted wage fixing. Offering benefits was a way around the law.
> Of course, once a benefit becomes the norm, it's almost impossible for individual firms to not offer it.
The real reason is that health insurance paid from pre-tax money by the employer makes it cheaper than being post-tax money by the employee. It's the tax system that binds workers to jobs via health care benefits.
Another reason people want wage increases in the form of employer-paid benefits is then they get to lie about the terrible pay they get, because they never ever account for the value of the benefits.
For example, whenever the teachers complain about their salaries, never mentioned are the generous benefits package they get.