Disclaimer: I have been away from KGS for six months, so some of the details I talk about may have changed by now, my apologies if that is the case!While I appreciate the mature attitude and more relaxed way of handling this (after all that is a big part of what sets KGS apart), I also do feel that the current system promotes aggravation too much. Aggravation leads to stress, and that leads to heated tempers.
Details could go a long way to mitigate this, without changing the underlying philosophy. For example, the already mentioned popup dialog should be changed to a more reassuring message. I still remember the angst I felt the first few times, when I tried to close a game my opponent escaped from and the warning dialog popped up. Was I really allowed to just close the window? Or would I have to wait for some kind of timeout, like on most other servers? Would I be labeled an escaper myself, if I just close the game? Or would it be counted as my "consent" to adjourn the game? Not a big deal once you know exactly how it works, but details like these do matter, and it is easy to lose sight of how they are perceived by a newer player.
Most of the time when your opponent escapes, we know that it most likely wasn't a fluke, because of the timing when it happens. So there is no point in waiting around, wasting our time even more, and the current wording makes it sound like we do something wrong if we don't wait for the other player to return.
Conversely, while I understand the issue of disconnections, what is the purpose of allowing players to just close the window and start another game? That is just absurd, and no amount of zen philosophy suffices to justify that.

There are two things wrong with that:
1) Closing the window is handled the same way as a disconnect. Why? Of course you can always just plug the chord to have the same result, but the barrier for that is a lot higher than just pressing the "exit" button. Wilfully closing/adjourning the game should simply never be possible, unless the opponent agrees to it. This is rude and unnecessary. Rudeness creates aggravation, so why allow it?
2) I also perfectly understand that you can start a new game after you disconnected, as your opponent may have left or started another game. But what is the reasonable explanation for allowing an escaper to start a new game, when his previous opponent
is still waiting on the board for his return? This is one of the rudest things to do, and from what I can tell, it is also absolutely unnecessary to allow it. I can't think of a single legit use case where this behaviour is helpful or just. Frankly, I think that if you join the server and a game you escaped from is active with the other player still waiting, you should be forced right back into the game. No other options necessary.
None of these things fundamentally make a difference, as the same rudeness can be expressed in more devious ways (and thus I understand if it has not seemed a priority to do something about it), but I hope I was able to make my point that it leads to unnecessary aggravation if such rudeness is explicitly allowed by the mechanics.
Changing these details would be possible without changing the system itself and the underlying philosophy, and I believe that it would help create a calmer, more relaxed atmosphere.
Other than that, the only major improvement I would wish for would be the possibility to request a manual adjudication of a game, to immediately score adjourned games if the outcome is already obvious.
Of course this is a question of manpower (unless it is volunteer based as on the free chess server FICS), but if it would at all be possible to provide this service for a fee (e.g. for subscribers), I would gladly sign up for it.
Thanks for listening!
