I believe the reason that the codes aren't etched into the metal is because common medical imaging equipment could read the code without removing the holo.
I doubt that any available medical imaging equipment is sensitive enough to pick up an etched engraving. In the first place, x-rays are very low resolution. CT and MRI don't work with metal objects because of extensive scattering and noise.
When you engrave characters to metal, this changes the metal's shape, making the characters clearly readable with pretty much any sort of reflective radiation. The tamper proof case may look great but what if tampering is unnecessary because any physician can take it to work and see through the case with medical imaging gear? An engraved secret in a metal coin is also going to be vulnerable to magnetic imaging techniques.
Yes, the metal's shape is changed...but the imaging equipment is not nearly sensitive enough to pick up etched characters on a coin... we're talking perhaps two thousandths of an inch in depth. Medical imaging equipment could determine the difference between a 50 cent piece and a silver dollar, because of size. It could not differentiate between a Canadian quarter vs a US quarter, let alone etching on a coin's surface... not even close. Furthermore, MRI and CT cannot accurately image metallic objects because of extensive noise and scattering.