I've spent some time thinking about different startup ideas / permutations to address exactly this solution. In my research, I've found attempts at both methods you describe above, in various forms and various states, with widely varying degrees of success, but most have ended in failure. The "successes" tend to offer some limited choice in plans, but the rates certainly aren't great and the deductibles are still pretty high -- mostly it's a fallback safety net for serious emergencies.
I think a startup that can help tackle this issue would create tremendous value in the payor / consumer market, but the field is extraordinarly complicated and requires a very rare multi-disciplinary background in individual state law (CA's system alone is very different from, say, MA's bc CA is HMO-based and MA has a public option), behavioral economics, gov't regulation, insurance underwriting methods, insurance administrative practices. Oh, and if it's a tech startup, the team would obviously need web dev / product skills as well.
The problem is, developing a basic mastery of all these subjects takes a lot of time -- reading, thinking, and experiencing to understand the pain points deeply. That tends to cut against the stereotypical startup team of two young twenty-somethings hacking away and living on ramen, who have never studied the insurance industry or directly experienced the pain of searching for or relying heavily on health insurance (bc young 20 somethings tend not to have major health problems). I think that's a key reason why startups haven't done much innovation in the insurance payer market.
My latest line of thinking is about whether there are hacks around the problem that can incrementally chip away at and disintermediate insurance payers as the sole gateway to affordable healthcare.