> they worked just fine before government started intervening somewhere mid-last century
Healthcare industry as we know it today did not exist back then (the costs and available treatments are on another level).
> b) their mechanisms (price signals, competition, law of supply and demand, etc) apply just as well like for any other essential goods (food, water, fuel, etc).
Not really or only in a very superficial way and extremely basic way.
> While regulations - brought for our own good and safety, of course - succeed in increasing costs and add delays. Just see healthcare, housing and education for some sad examples.
As far as healthcare and education are concerned this is almost entirely an American problem. Some countries like Switzerland or the Netherlands have entirely private/non-state run healthcare systems but extensive regulation has kept costs relatively low and accessibility at very high levels.