HDHP plus great price transparency (especially pre service, where one can potentially cross-shop providers, vs. being in a facility and given only one option) would be good for cost reduction; if you can't surface and measure the costs, you won't have any incentive to lower them.
I personally have a fairly mediocre $230/mo blue cross plan in Puerto Rico which largely only covers care within Puerto Rico (and which I've never actually used for anything), and rely on medical tourism where I pay 100% out of pocket, and until Amazon bought them, OneMedical for cheap clinic care which I also paid 100% out of pocket. I previously had a WA state HDHP for $100-200/mo pre-ACA which was great but ACA killed those/insurers left the state.