The double edged sword of not understanding the difference between copyright and trademark, and not knowing what the Red Cross actually does. I've seen people argue that it's a good thing when games use the red cross to denote healing, because it trains people to recognize it as a healthcare symbol. The Red Cross does much, much more than provide healthcare...

It seems that neither "copyright" nor "trademark" are necessary for this conversation.
At https://en.wikipedia.org/wiki/Protective_sign I found these sources:

Misuse of protective signs, signals, and symbols in order to injure, kill, or capture the enemy constitutes an act of perfidy.

States party to the Geneva Conventions have the obligation to adopt laws and sanctions to be enforced before national courts that prevent and punish the perfidious use of these emblems in times of peace or of war. To implement such measures, domestic laws must be adapted to integrate the protection of these emblems.

It seems that https://www.congress.gov/109/plaws/publ366/PLAW-109publ366.pdf is what is referenced by https://en.wikipedia.org/wiki/Military_Commissions_Act_of_2006#cite_note-1

Any person subject to this chapter who, after inviting the confidence or belief of one or more persons that they were entitled to, or obliged to accord, protection under the law of war, intentionally makes use of that confidence or belief in killing, injuring, or capturing such person or persons shall be punished, if death results to one or more of the victims, by death or such other punishment as a military commission under this chapter may direct, and, if death does not result to any of the victims, by such punishment, other than death, as a military commission under this chapter may direct.

I assume that a country that does not enforce international law is more likely to be affected by UN peacekeeping operations, which probably makes enforcing international law vastly preferable: https://www.ibanet.org/article/CEBC5F69-A238-49BB-B85A-5E8D878FE485

Whether it’s copyright or trademark is completely inconsequential. The point of it is to stop people from diluting the meaning of the Red Cross, which literally gets members of it killed in conflicts.