There are plenty of ways to collect said information, it isn't a couple of log files that are going to save anyone.

Try to live in a society where everyone, including your closest family members, might collect such information.

https://en.wikipedia.org/wiki/PIDE

This still requires the adversary to coerce your friends/family members into snitching on you - it involves effort and risk for them and doesn't scale.

Compromising a telemetry server is a one-off operation, would work at scale and is much less risky as the targets have no way to detect it.

Some never needed to be coerced, that is the whole issue.

With that, I would say good luck troubleshooting your server if you don't collect any logs whatsoever. I wonder how you would even protect against bruteforcing and DDOS attacks if you never stored IP addresses for any amount of time.

But unlike a server, a desktop app isn't vulnerable to any of those issues that would require logs to defend against.

The issue here is that the server you downloaded the desktop app from is. You can reduce the amount of this you have to deal with by shipping a native app, but you can't get rid of it entirely as long as you plan to host a web site or a download of something, or if you plan to let users communicate useful things back to you (such as their hardware specs, OS version, crash reports, usage patterns, etc).