I've worked for the non-profit insurance subsidiary of a charity hospital system, and part of the problem is that ANY of the competition is for profit. What that means is that the for-profit companies are effectively setting the baseline of coverage. Healthy people (or the HR department at the company) aren't as concerned with richness of benefit as they are with the lowest premium. Sick people, though? They've got a list of doctors and drugs they want to make sure are covered. So if the non-profit benefit is too rich it attracts all the sick people and suddenly the operating costs of the non-profit skyrocket and they go out of business. It's a weird model that can't be AS good as the mission wants to be.

In my case the hospital system actually created a generic drug manufacturer themselves to undercut for-profit drug manufacturers. THAT was less daunting than trying to impact the insurance side any more than they already do.