Possibly unpopular opinion: the red cross and red crescent symbols shouldn't have the legal restrictions:

As specified by the Geneva Conventions, the four recognized emblems are to be used only to denote the following:

• facilities for the care of injured and sick armed forces members;
• armed forces medical personnel and equipment;
• military chaplains;
• International Red Cross and Red Crescent Movement organizations such as the International Committee of the Red Cross (ICRC), the International Federation of Red Cross and Red Crescent Societies (IFRC), and the 190 national Red Cross and Red Crescent societies.

The rationale here, I think, is that there needs to be a simple symbol marking the things-you're-not-allowed-to-attack. So, military chaplains get included because they're noncombatants.

But also, the symbols are:

to be worn by all medical and humanitarian personnel and also displayed on their vehicles and buildings while they are in an active warzone

So, say I'm an ambulance driver. I was going about my regular civilian business in my regular civilian ambulance marked with the Star of Life, like it's supposed to be. Suddenly, there are people with guns running around. I guess I'm in an active warzone now! People start shooting at me because my ambulance doesn't have the right symbol on it.

This is kind of a dumb scenario, but it gets at a real thing, which is that it seems pretty weird to limit the symbols' usage to specifically military medical facilities. The key thing is that they're medical facilities, not that they're armed forces medical facilities.

Civilians understandably don't know about these restrictions, and the red cross symbol gets used illegally all over the place. And, imo, yeah it totally should get used all over the place for civilian medical facilities. It's instantly recognizable and simple, as it was designed to be, and it's actually important that there be a symbol like this that applies to both civilian and military medical facilities.

Maybe there's something important that I'm missing, here?