The other issue is that cutting it out and replacing it is the only option when the battery dies or goes wrong. If the product/company dies in the meantime, you have a bunch of scar tissue and no hearing. Replacing the "normally inside" bits of a cochlear implant is really high risk of not working as intended, so changing brands isn't a small ask. You really get to do this once. So putting the processor inside and tightly integrated with the nerve stimulation seems inadvisable. At least with the processor separated, you have a chance a compatible replacement processor could be made and exchanged without huge risks.
From "Trends in Cardiac Pacemaker Batteries" (2004) [0]
The first implanted cardiac pacemaker used nickel-cadmium rechargeable battery, later on zinc-mercury battery was developed and used which lasted for over 2 years. Lithium iodine battery invented and used by Wilson Greatbatch and his team in 1972 made the real impact to implantable cardiac pacemakers. This battery lasts for about 10 years and even today is the power source for many manufacturers of cardiac pacemakers.