I wear one now because my wife insists and its a cheap and easy thing to make her happy, but I still think they are a bit silly.
1. Biking is really not that dangerous. Accidents are extremely rare. Its not like we're base jumping.
2. When an accident does happen, its even more rare that the rider is incapacitated.
3. If I am incapacitated, its even more rare that my ID and Credit Card would go flying off me or the bike.
4. If the accident is severe enough that paramedics are called, chances are good they'll have a few seconds to go through my pocket.
5. If they don't have time to go through my pocket, they will still do everything they can to save my life and get me to the hospital.
6. Once I'm in the hospital, they are going to want to know who to send the bill to. The ID I had in my pocket will quickly be found.
