Based on the explanation given, there's absolutely no privacy benefit to not including this code. The fact that it's Terraform doing the work is already being sent via the User Agent in the API requests. The fact that it's _you_ who is making the API calls is also embedded in the request. This amounts to a minor hack of Azure's API logging to enable slightly more convenient reporting. It sends no new data. In other words "opting in" or "opting out" has zero impact on whatever privacy implications you are worried about. This comes down to a simple misunderstanding of what's going on.
Given the amount of fingerprinting and screwing with the content based on platform, I'd be happy to do away with user-agent completely. I'm tired of websites that are completely broken on mobile and force you to use the app (or constantly remind you about their app) and everybody returning a globally unique identification which is so hard to scrub.
Because for this specific bit of data, the value that it's set to by default has zero privacy impact whatsoever. So getting upset over nothing and yelling at a CEO who gave a great explanation of what's going on is incredibly counterproductive behavior.