Ultimately, the problem is much bigger than /etc/machine-id since there are dozens of hardware IDs on any PC that can be used by malicious telemetry to silently to uniquely identify and track you, and the only solution to this problem currently is to make sure you really trust any software you use.
Systemd, in particular, acts a lot like malware for Linux because if you try to reset your machine-id a long list of stuff that breaks in in it. You could make a cron script to reset /etc/machine-id every day, but machine-id is so deep in the stack that you’d also have to reboot to ensure it’s updated.
Wat? If you have something running on your system that’s tracking you, you are already fucked. It doesn’t require that file. It can just create one anywhere on the system and use it, if need be.
A browser is one example, what’s the alternative to that other than sticking it inside some sandbox or something?
Sticking it into a sandbox is reasonable, but you can also use more privacy aware browsers like LibreWolf. Chrome and Chromium will track you 100%, so don’t launch those unless necessary.
At least that’s what I do.
The problem with machine-id specifically is that it’s become a standard way for the browser to identify itself. There obviously other ways you can be tracked, but this is a very low bar and a common way of sites tracking people.