The Wikipedia page also explains why the phrase came into use and what it was for.
Lawyers don't like novelty. Novelty is always a source of uncertainty, and clients don't like uncertainty.
So if a clause reading "Trap no beagles forwards the staff quarters" appeared in the previous fifty contracts, then by default it's going into the fifty-first contract. That is true even if the other fifty contracts had that language purely as a result of a copy-paste error by a clerk. Because those contracts worked, and we want the new contract to work too.
Unless/ until there's a case where "All rights reserved" is found to screw things up for the client, no lawyer anywhere is going to go out of their way to recommend that you stop writing that on things /even though it now makes no difference/ and remains purely by superstition. If you're the client of course you can ask, and a good lawyer will say "Yeah, that's just superstition and we can remove it" but if you don't ask they certainly aren't going to suggest you go without the magic talisman.
It's not just lawyers, this happens on our home territory -- people who type "sync; sync; sync" for example; and in medicine -- NICE has a Do Not Do list, of specific things practitioners do that are not known to be effective but people do them anyway; and no doubt many other fields.