Once something is integrated, there is always a possibility of bugs. You have a setting that says you are not allowing some feature, but the bug creeps in and the feature ends up enabled behind your back.
Another problem is that with AI, companies have incentive to make "bugs" and use anything they can get their hands on for training. Your data is the product. So while you may be fine with some parts of your code being used for training, there will be parts you will want to keep secret for security reason (if nothing else, various API keys and similar), but if you have AI integrated in the IDE, you can never be sure which parts of your code will be used for training and which ones are not.
For some people and companies the security concern is real and even slight possibility that some parts of their code or other information can leak through AI can be a huge risk.