I had and recommended a variety of non employer provided plans over the years. If I recall, the biggest concerns were always pre-existing, and cost. pre-existing was helped with obamacare. However I only did that because I didn't have employer insurance. I don't really get the "shopping around" for health insurance. Care, yes, insurance, no.
The issue then becomes that the employer isn't going to reimburse you their spend, if you don't want their insurance but instead want to buy it yourself. And that's way too expensive (since it's already factored into your salary/benefits package...)
So there is plenty of competition out there, it's just that we can't pay it with the current employer funding models in most cases.
From what I understand the entire employer provided benefits was developed way back when, in an effort to stave off government healthcare and unions...basically private business said it will provide for people, to cut out gov/unions from trying to squeeze in. This was back in the days when employers were committed to providing job security, benefits, and people could raise a family off their one, average salary (summarizing). Since business has moved far away from that model, and it's now "on demand employment", it's obvious we need the safety net for healthcare IMO.