This would eliminate the many-to-many negotiation problem that contributes to absurdities like Duke University Hospital having 1,300 billing clerks for 900 beds (https://www.pbs.org/newshour/economy/why-does-health-care-co...). It would also make it much easier to estimate costs before going to a provider, because instead of having 1000 different prices, that service will have one price (albeit with some variability depending on what's actually done).
If you paired it with a law that mandated that hospitals publish their prices for services in a simple JSON format, such that companies could use it freely to create price comparison tools, suddenly you'd make it much easier for market forces to push prices down to sane levels. It's insane how difficult it is currently to figure out how much even routine and planned operations like delivering a child will cost, and as a result people don't bother to even try, so there's no incentive for hospitals to keep their list prices anywhere near the realm of sanity.