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.
Systemd was designed long after a lot of these security practices and problems with tracking were well understood. There’s very little excuse for it doing a lot of the things it does. Systemd is literally re-architecting how Linux was meant to work originally, and for the worse. I get the impression you’re not actually familiar with the history of Linux or Unix philosophy in general.
Having to put everything into containers is really just a work around bad architecture that keeps being pushed in the Linux world. Containers are useful, and probably the only way to actually keep apps from having too much access to the system at this point, but I don’t see why bad architecture should be accepted and then have to be worked around.