If they do that and all the ambulances, hospitals etc. change to the new symbol, that symbol will have the same problem in a few decades because it will be similarly omnipresent. Considering it’ll probably take about as long for all the equipment and buildings to relabel, it doesn’t seem like a practical solution.
>>johnco+(OP)
I don't think that's likely to be the case. A red cross has already become established a generic symbol for medical things. It is unlikely that would change if the Red Cross organization changed its logo.