Delete PMs from both users involved

The only reason you want such a silly request is because of your own selfish reason to hide what ever it is you don't want seen, that YOU mentioned or brought up in some kind of fit, or "accidentally" typed it (in a conscious and coherent manner, mind you).

This isn't even a logical suggestion, let alone one that has any use for anyone else on the forums, bar anyone else with a mindset like yours. Imagine if someone sent you some hate mail via PMs, and you wanted to report it, but they deleted it. Then what? Your idea backfires on you, and further reinforces the pointlessness of it.

Auto-deletion of old PMs is one thing. It's entirely possible they already do that, without informing the users. That's perfectly suitable, it benefits the system and it benefits users who are in the present and in the now. Your previous idea only supports you in your own selfish fashion, with which a simple cure is to simply take a step back and prevent yourself from writing what ever it is that needs to be so carefully hidden in a PM of all things (which is still going to get read by someone, the point of PMs).

TL;DR, this idea is self-centered and benefits only one side and on top of that, it's asinine. If you don't want a sent message to be read by others, don't send it in the first place.