This is a recurring topic. Of course each person must make their own decision. In my case I think RoadID and things like it are awfully expensive for what they do and they don't have any enforceable privacy gurantee.
Medical issues are only one reason to carry ID and may even be the less frequently needed reason. Many states require positive ID when entering places, when stopped by law enforcement, in event of an accident/incident even if the person is merely a witness. In most cases that means a government issued picture ID. In my state and I think many others in addition to a Drivers License a person can get an ID Card. In my state it looks just like the drivers license but doesn't have any of the driving privileges, etc on it. I carry that for TSA and any other ID requirement not involving operating a motor vehicle.
The other thing is identity theft risk. Anytime someone can call in to a place that has your medical records simply by giving a registry number, like RoadID, you can bet someone will use it to get access to your info. How many times in the past year have there been losses of literally thousands of personal records from businesses and government agencies? Answer is many.
Get a picture ID; hang it around your neck and have all the bases covered. Cheaper too.