I agree there is complexity cost, but that doesn't mean you can't benefit from it if you generally can navigate said complexity. I've never had issues getting reasonable price estimates from independent doctors (large systems refuse to reveal their negotiated rates) - emergency situations are certainly costly, but under a plausible worse-case scenario I'm still solidly saving having an HDHP.

Ironically, the whole point of HDHPs was to put downward pricing pressure on the medical system by encouraging people to price-shop. Alas, due to a variety of market/regulatory factors, that hasn't happened.