There's nothing stopping a person from creating that. You'd package it up and get it added to the Debian, Ubuntu, RedHat, etc. repos and people would be able to install and use it. That's about as close as you'll get to having it generally available for all Linux distros.
Personally I don't see the value, and think it's invasive, so I would never install it, but people who wanted it would be able to use it.
The telemetry proxy service would need packages for each distro, including scripts to work with systemd and init, and maybe a "libtelemetry" package to make using the service easier.
The way I see it working is that if the system service isn't installed, isn't running, or has remote telemetry turned off then the commands for sending telemetry will succeed but send the data to /dev/null. Otherwise the data gets anonymized and uploaded to the user's configured telemetry host.
It could almost be built on syslog, now that I think about it more, but that would be terrible.
This page from Debian Wiki may be interesting to see what all is out there: https://wiki.debian.org/PrivacyIssues
I enable it on my personal production systems and disable on everything else, both on privacy grounds (work), and not providing wrong data (disposable VMs).
This is the right approach.
Love the idea!
Privacy should be privacy by default, and if you want users to send you crash/usage logs then you need to show them all of the dirty details, let them review it and chose whether or not to send.
This service would be guaranteed to be unidirectional, would store data publicly on non-profit-run servers and domains and fully comply with GDPR (by not storing any PII and ano/pseudonymising everything).
Developers would connect to this service over dbus and consume the uploaded data in daily batches.
Hosting and hardware fees would come from donations by distributions and other organizations distributing money to the FLOSS ecosystem.