Yes - the reason why health insurance is so pervasive as an employee benefit is that it can be written off with no taxes, whereas currently this kind of monthly-fee unlimited visit medicine can't. That's asinine from a tax perspective, but that's how the current system works.
The origin of health insurance as an employee benefit in the US is that during World War 2 wages were fixed, so employer provided health insurance was a government approved way to give more to the employee through benefits. Basically it's a bad hack to get around a bug.