That is actually an old legal trick. By mailing something to yourself you are getting a sealed envelope that is dated by a government agency. If you want to prove that you had or knew something at a particular time (like a copy of a will or a statement by someone) then it is a useful scheme.
If your post office is accepting open envelopes then they need to stop doing so. It's not just against various rules but can jam the machines that sort envelopes.
You could tack it shut just enough to get by, but not actually full seal it. For that matter, you could probably just stuff the outer flap down inside the envelope and maybe put a very small piece of tape on it. Same difference in the end. The point being, mailing yourself an envelope doesn't really prove anything about the provenance of whatever is found inside later.
I guess you could tape it shut and then carefully remove the tape when you get it. Once you have something you want to "send to the past" you use whatever natural stickiness comes with the envelope.
I've gotten a decent number of envelopes where the flap is simply tucked into the envelope rather than any attempt being made to seal it. It's all been junk so if a few come apart they don't care. I believe there was some rate advantage to doing it that way.
So I wrote my landlord’s address at the top and my address below it, stamped it and happily posted it.
Sure thing after two days I received in my mailbox my check /facepalm