It’s not quite that simple. Helmets are deterrents - Melbourne is a fantastic example where cycling is less common than it should be and public bike schemes keep failing specifically because of the requirement to wear a helmet. Companies like Lime try to solve this by attaching a helmet to the scooter. 90% of the time the helmet is missing. Yeah I could spend 30 minutes walking to every scooter in the area trying to find one I can ride legally, or I can just get an Uber.
When people are deterred, they take less eco friendly forms of transport, and are less active. This has negative health consequences, although difficult to measure and compare. But it’s not black and white.
The entirety of Europe gets by perfectly fine with public healthcare and no helmets. So I don’t buy the argument that this is truly a problem for healthcare.