Zero for a draw is way too radical !

There are tournaments where a draw is given a zero score and only wins count. I sympathize with the intention but there are far better ways to encourage fighting chess. Sometimes the guy who draws really did fight his hardest. So why not be a little less radical ? Stalemate could be 2/3 of a point and for the player without a move, 1/3. That could motivate a player to play on when he might otherwise shake hands to split the point. Perpetual check might also be worth 2/3 of a point. 1/3 to the harried King. 

This scheme also preserves the one game - one point tradition. 

I've never heard of this scoring method. I am only familiar with using the  3/1/0 system to promote fighting chess.

I disagree with the perpetual check one, perpetual check is usually a way to SAVE a draw, and the point difference for stalemates encourages stalemating

A stalemate being worth more than a draw, but less than a checkmate probably seems radical to most people, but actually makes quite a bit of sense. I've heard even the likes of Capablanca and Lasker have argued for it in the past.

The rule of thumb in endgames is that a 2 pawn advantage is required to force checkmate, with a 1 pawn advantage only enough for a stalemate. But in super-GM play, where draws currently dominate, gaining a 2 pawn advantage is no small task. Players should be rewarded for having outplayed the opponent to the tune of 1 pawn.

Of course, this would drastically change chess, and perhaps not for the better, though it would be an interesting experiment.

There are two different issues here, let's not mix them up.

One is whether stalemate should be worth more than a "regular" draw. Well, maybe, but it would change a lot of the current endgame theory, for instance rook vs bishop would be a "half win" whereas rook vs knight would only be a draw.

The other is how tournaments should score draws. I have never seen anywhere the "draw=loss=0" system, but I have seen the 3-1-0 in use and it works pretty well.

Also notice that actually, a stalemate is more likely to be the result of some "fighting chess" than any other kind of draw...

I actually like 3/1/0 scoring, but IMO stalemate should be scored the same as any other draw.

The 3-1-0 system has merits when used in occasional events. I would hate to see it become the norm. Other alternate systems are like chess variants themselves--a diversion from the search for truth in chess.