Plus, when you write software that disrupts an industry, your employees are still software developers who work and function like software developers. If you want to change healthcare, you need to change how the doctors operate.
That's called Fee-For-Service (FFS) and is there is active effort to replace it with quality-based schemes. Providers still get paid for individual services but the rate depends on quality metrics of their overall population. (Source: worked in software for Population Health)
The inefficiencies you describe are less from the clinical side and more from the administrative side. Many of these admin-level people are doing what they can in an incredibly complex maze of processes, most of which started for a good reason. But they are process bees, and unable to make any changes: there's a huge barrier to change as of course nobody wants to be responsible for worse outcomes / deaths due to failure to respect process—yet they are immune from repercussions if poor outcomes are cause by said process.
More to the point, clinicians live in a constant grey zone: everything is a risk tradeoff and they do what they can to get the best outcome. The adminstrative folk see things in black and white. Here's a real example: outpatient office has slightly expired meds that are life-saving if a procedure goes bad, but new meds are not available because factory got damaged by hurricane. Common-sense is that a med does go from perfect to useless overnight and a few weeks is no big deal, especially when there is no alternative. Administrative view is the meds can't be used and must immediately be discarded because having them around the office will expose them to liability during audits... yet of course doesn't understand why that means all procedures of that type would get cancelled.
So much in medical diagnosis is just a very coarse decision tree and it is uneconomical to investigate every sickness.
Imagine doctors having more time per patient. Imagine many diseases detected before there are symptoms.
I got carried away here, but medicine looks so much more promising then CS sometimes.