I think you should be able to load whatever software you want on your phone (though technical speed bumps are good, imo).

But this is far from the biggest problem in this story.

e.g, if it’s important to be able to access the information available through the app, why is it locked?

Why isn’t that important information available on a regular web site?

Why do you need to install an app before getting emergency medical attention, anyway?

While sideloading might let you work around a broken bureaucracy from time-to-time, that’s not a very effective way to improve the system.