https://www.bradley.com/insights/publications/2012/04/one-cr...
In my unprofessional opinion, the red cross should go the way of "tissue", "google", "coke", etc. It's too common, hasn't been enforced. You lose the exclusive right to it.
This isn't some bit of copyright law. This is an international treaty that has vested the right to enforce this thing with a specific group. Misuse isn't going to result in in a DMCA takedown. Misuse of the red cross is an international crime, a violation of the Geneva Conventions. Don't like it? Elect people and have them withdraw your country from the Geneva Conventions. I doubt any party anywhere would ever adopt such a platform.
Prison Architect actually received a notice about this. Their answer was very simple: replace the red cross with a green one. There is no reason other games cannot also make this very minor concession to the Geneva Conventions. It is the law.
Look to TV shows. It is very very rare to see an actual red cross. Ambulances on shows like Scrubs don't use them. Film/TV people know to respect that symbol and only use it in very specific scenarios. MASH used it extensively, but then too very carefully.