The rules are all arbitrary, but they're also fine-tuned to make for an incredibly beautifully balanced and complex game. I think removing stalemate would deprive the game of much of its balance and nuanced complexity.
I tend to view stalemate as a very specific type of fortress. One in which the king's inability to move into check is what ultimately provides his protection.
That's my point that this stalemate rule is arbitrary.
True.
So is the rule than the knight moves in a L-shape.
The board could also be spherical and made of leather and be sent by teams of eleven players into the opponent's camp. That would just be another set of arbitrary rules, but somehow it's not called "chess".