It is a brilliant discussion on so many levels. On reflection, I think the rule is great and some of the people in the forum above made some excellent points. Chess is about material AND position. If you do not demonstrate an advantage in both, you don't deserve to win! That is what the stalemate rule actually says. Beautiful!
One of the comments in the forum above is relevant to Chess960:
"If k+p vs K was always a win, I think most people would adopt a more conservative strategy: don't throw a pawn away in the opening for some initiative, because that pawn is going to come back to haunt you. My own game is based on a lot of semi-sound gambits, which I play with confidence because I recognize which pawn endings I can draw and which I can't - so when my gambit fizzles out, instead of resigning, I start maneuvering towards a drawn endgame. Removing stalemate would make that strategy untenable, and would mean that gambits were much less playable. I'm pretty convinced that's a bad thing."
That is a good point. Thankfully in Chess960 we do have stalemate! If we didn't have a stalemate rule, a gambit line in Chess960 would be even less likely than it appears to be at the moment. As it stands gambits are already rare in Chess960 as far as I can tell. I think that it is because without previous knowledge of the results of a gambit line, players like myself are unlikely to try them. That will change with time as people start to get comfortable with the conceptual thinking that Chess960 encourages.
Here is an example gambit line in the one and only time that I have played one:
SP039: A Queens Gambit Opening without a C1 Bishop!
The line produced a beautiful open game and an aggressive attack possibility on the g-side. It is very funny considering it's initial similarity with the SP518 version of the Queens Gambit line. But the point is that this gambit does not guarantee a likely return of the pawn as does the SP518 version. If that is true, then indeed would such a gambit be played if there were not a stalemate rule?