I do not know what the laws are regarding wearing a radiation badge in the scanner. I suspect that TSA would use the excuse that it could be hiding something (same reason they make you empty your pockets of anything, not just metal). By definition the device would need to absorb some energy and thus could obscure something behind it.

I suppose it would take quite a bit of lobbying for TSA to certify some type of device, likely similar to those that are given to parents who need to hold their children for x-rays. From an individual's standpoint, it's probably just as accurate to simply find out what the radiation dose was for the examination (it should be recorded by the machine) and recording the cumulative dose. A colleague of mine helped develop an interesting iPhone app called Radiation Passport that will calculate your increased risk for cancer, cumulative radiation, etc. based on a number of activities including airport scans and medical imaging.

Personally, I always opt out for the pat down. I am a radiologist and am exposed to quite high levels of radiation, though we take every precaution to limit our exposure with shielding and distance. Though I agree that the exposure to any one person is probably negligible except for the most frequent flyers (particularly given that each pass through precedes a flight that likely results in more radiation), the fact that TSA continues to use metal detectors indicates to me that there isn't enough of an advantage.

On principle alone, I cannot agree with going through a screening exam that results in radiation exposure when an apparently equally good exam is available that does not use ionizing radiation. I would actually be more willing to go through the backscatter scanner if TSA stopped using metal detectors completely and told me they were inadequate, because the safety of using a superior screening examination would be worth a few micrograys of radiation.