This is a common approach to "privacy" taken by orgs like Google.

You don't get to access or export your own data in order to protect your privacy, but Google still gets 100% access to it.

Some messaging apps do the same and won't let you take a screenshot of your own conversations. Like, someone sent me an address, but I can't take a screenshot to "protect my privacy".

Imagine my surprise when I attempted to record the iPhone mirroring application, which was running on macOS. Apple did a great job on their DRM because I simply recorded a black screen while I was attempting to play back a video from an app on the phone.

I'm sure it's given some businesses the confidence to invest in iOS app development, but it felt bad.

Which messaging apps are those? I have only seen such behavior for one-time photos, where it makes sense (although one-time photos are security theater because nothing prevents you from taking a photo of the screen with another device).