TL;DR: Placing it in the chest or abdomen actually makes perfect sense.
There are several reasons why your ideas won't work, at least with current technologies.
why not either a) have the pulses be generated directly adjacent to
the electrodes, instead of having the IPG somewhere in the chest or
the abdomen
Because IPGs are the size of pacemakers, and you can't put an object that large inside the skull. There is no spare room inside the skull, so it would displace brain tissue, possibly causing injury, and it would be a much more difficult surgery with much higher risks. I would imagine that placing a tiny electrode and wire deep in the brain is difficult enough, but placing a device the size of an iPod would be vastly more difficult and dangerous.
Thanks to pacemakers, putting it in the chest or abdomen is perfected surgery that's performed hundreds of times a day worldwide in an outpatient setting with very low risk and an easy recovery. It makes perfect sense to put it there.
Image source
or b) have the neurostimulator on the body instead of in the body,
with the leads going transcutaneously to the electrodes?
This is addressed in comments by two people:
bob1 points out maintenance and external wires. Replacing a battery buried deep in your brain would be a major surgical procedure with significant risk. And having an external wire that can be caught on something and yanked out of place in your brain could have catastrophic consequences. Suffering brain damage from combing your hair seems an unreasonable risk.
Ian Campbell points out that having a wire going from your skin into your brain would be a major infection risk. Any external pathway from the outside world into your brain is dangerous.
