My company produces brain implants. Technically you can upgrade the firmware wirelessly (we do this in testing all the time) but nobody wants to take the responsibility for doing that with patients. With more RAM available I think wireless upgrade will be the standard in a few years.
Wireless updates obviously have major security issues, but I wonder if there's a compromise that doesn't require surgery. Induction, perhaps? Updates transmitted through a wired induction pad pressed against the skin above the device?
I don't know the details but the biggest problem seems to be the interaction of the pulse generator with the leads. You can't shield that away. It's more complex.
For a wireless update you need to be able to store the new firmware in a temp area, verify it and then activate it. Old devices don't have enough memory but that's changing. Also, most new firmware needs new hardware features so this capability may not be that useful in practice.
It's more than liability, reducing physical access requirements opens up a much larger attack surface.
I know if someone's opened up my skull. I assume everyone has some sort of multi-band wireless transceiver in their pocket, because that's a cell phone.