I think you are conflicting some things.

The analogy you used doesn't quite work, because you are not telling everyone at the protest where you live. A more accurate analogy might be you going to a protest, loudly saying something which you later regret, and then ask everyone to just forget about it and delete any footage you might be on. Some might comply, but many won't, and you won't have any idea who didn't.

Furthermore, "people with the knowledge and resources to run their own servers" would be no more safe than you are, because other servers (instances) will still record whatever they post out there. If I make my own federated server and send out a comment, other instances that federate with mine will receive a copy of it. At that point I can ask them to delete it; however, even if they do comply, there is no guarantee that another user hasn't made a local backup of the comment or just screenshotted it.

At the end of the day, tech isn't magic. Everything has limitations, and you can't do everything at once. You can't have a system that allows you to make public comments that go out to several servers where it is shown to thousands or millions of people, and at the same time expect to be able to delete all of it when you feel like it. Tech can't do everything, and at some point we need to take agency and accept responsibly for what we put out there.

Finally, I'll add on what another user said:

Opposite to Instagram or Facebook, on Lemmy or Mastodon you can create an anonymous account. Yes it will be logged (normal public internet), but you won’t be treacable. The UI doesn’t have any tracking scripts, and many instances don’t require an email even to sign up. Use the Tor browser to spoof your IP.