Interesting idea. Current battery in the device (I looked it up) is:
Chemistry: Lithium carbon monofluoride
Voltage: 3.3 V, open circuit
Rated capacity: 1 Amp-hour
Self-discharge rate: <1% per year
Its a tiny non-rechargeable battery presumably carefully picked for safety and very slow usage over several years.
I suppose the main barrier to wireless charging of implant batteries would be heat - wireless charging generates heat. And when something goes wrong with wireless charging it can generate a lot of heat. So I guess its risky? But then surgery to change a battery is also a significant risk.
Also I guess someone would have to go through the long process with the FDA of getting it all approved, whereas (at a guess) people designing implants try and use already-proven components and techniques where they can to make approval more likely.
Could also just be a battery lifetime issue? 8 years is a long time. If they made it rechargeable, they might still need to replace it every 8 years anyway just for safety.