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.
for most desktop users, not persisting /etc/machine-id is usually fine, but there are some specific scenarios where it can cause issues. Systemd uses machine-id to tag log entries. If it changes, you might lose the ability to correlate logs across boot sessions in journalctl. This is mostly an annoyance for debugging rather than a functional problem. A few NixOS modules like services.openssh or certain mail servers use machine-id for generating default host keys or identifiers. Changing it might cause warnings on first boot after a change, but usually nothing breaks since they fall back to other identifiers.