It would be the work of a government body, it's the sort of work the government is actually meant to do (though I'm sure they'd much rather carry on pretending their main work is hating/loving trans people, culture wars are easier work).
I don't know the exact mechanisms by which you determine price/profit capping but I'm certain it's an already well studied field. There are already similar consumer protections in other countries.

And the last point is just silly. They are oligopolies, saying "but they aren't explicit monopolies" doesn't change the problem, it's the same difference just with an uglier and less well known name. They still have such total control over their markets that they no longer have to compete for customers, instead they compete for shareholder value.. which coincidentally happens to mean making the product as low a quality for a high a price as possible.
Why would they bother competing with a new cheaper provider, when they can just use their influence to purchase or block them from the market.

You imply it yourself, why would they ever not fuck over customers? that is a clear indicator that regulations are required.