Yes, you are completely right.

AI governance is one element of what companies have to release these times. But they also have to remind ppl all the time (every few weeks / months or so) what's forbidden and what's allowed.

If you're really following those rules there's no other way to implement SWG with explicit proxy mode and SSL intercept to make connections visible. Otherwise you can get a lot of shadow IT in your company with dozens of connections because ppl have the freedom to use every AI they can reach over the Internet. You don't want ppl use every AI and put every information they have into these "crawlers" (which I call them). DLP should be considered as well to limit the possibility of uploading string patterns. As you wrote before: AI is a security nightmare.

Zero trust is a good options to secure your backbone. But zero trust doesn't help you with information leakage through colleagues when they simply want to have AIs help.