What's weird to me is that insurance companies aren't at all incentivized to reduce costs. In fact, they're blatantly incentivized towards raising costs. It really doesn't matter whether they're capped at 20% profit - their profit scales with larger overall numbers, so they're incentivized to keep costs high and push them higher in all situations. If healthcare costs rise 10%, they can push their insurance prices up 10%, and have a 10% increase in profit, even under the same percentage cap. Doctors like it too, since they'd make an extra 10% on the same procedure. Even the patients, in most cases, care far more about quality care than about the cost of care.
Auto insurance and repair has plain old economics going for it - as spare parts become more available later in a car's production run, the costs drop. Home/flood insurance seems like it would be subject to the same upward incentive in home prices as health insurance, with the caveat that housing prices usually remain relatively stagnant outside of a bubble and there's not much the insurance companies can do to affect pricing anyway.
Healthcare, though, becomes a problematic outlier relative to other types of insurance - how do you lower costs when almost all the players have a tangible incentive to help costs rise and the ability to do so, and even the consumer has an ambivalence to cost as long as quality is maintained/improved and the cost burden doesn't reach a certain (unknown) untenable threshold for a large enough percentage?
That's the problem the US is attempting to deal with in healthcare, at its' core. It's probably the most complicated economic and policy problem possible - how do you regulate a market that has almost nothing providing natural balancing factors? Supply and demand are effectively nonexistent, healthcare isn't optional (and never really was, even before the ACA), and all the players are rewarded for pushing on the same side of the scale.