The reason you can get a written estimate is because there’s a big book the service writer flips to, “hmm, front swing arm bushings on a ‘12 Corolla: 2 hours. Front end alignment: 0.75 hours...” Worst case is, I get the acetylene torch out for those rusted-to-hell front end bolts, but it’ll take me about what the book says, usually less. Well, worst case is a bunch more front end parts are shot, waste of money to do just bushings, and customer doesn’t want to spend the money (after the requisite phone call). Bolt ‘er back together still broken, and send them on their way.
You figure out how to apply that same scenario to cardiac surgery, and you can have your written estimates.
Doctoring really isn't all that different in principle. The actuaries have these books and already do estimate these costs. And the overwhelming vast number of procedures are consistently predictable.
There's a couple ways of managing unforeseen issues, the simplest of which is to pad the total with a comfortable risk margin. Or allow extra billing for emergencies, but publish rates on how often they "miss" their estimates like restaurant health codes.
You figure out how to apply that same scenario to cardiac surgery, and you can have your written estimates.