That last post is assuming that there IS, in fact, a first-move advantage in chess.
3 points for a win, 1 for a draw

Maybe another rule, +1 for win, 0.5 for a draw but 0.1 for a draw before move 20 because it is not playing chess.

See, why should we care about GMs not playing chess? If they wanna draw before they play, so be it. The way I see it, unless you have invested time and energy to play chess at that level, you cannot complain about draws. If somebody offers you a quick draw, decline it. But it doesn't concern you when two strangers agree to a draw!

Regarding the topic the OP started: the 3-1-0 scoring system.
With respect to the current system (which is fine in my opinion), in the proposed system, if you lose a game you grant an opponent 3 points. If the opponent then loses the next game, in the current system he will have the same amount of points as a player who draws two games. In the proposed system he will have 3 points, which is more than the drawing player. On top GM level, the proposed system might even become counter reproductive as 'granting' an opponent a win is more valuable. Lines that give black solid drawing chances might even become more popular as losing the game costs more. The same for white, players might even take less risky lines as losing a game is a bigger problem. Winning a game is very good of course as you get more points but in chess, taking excessive risks to win a game is often counterproductive as you lose control over your own position
That last post is assuming that there IS, in fact, a first-move advantage in chess.
Everything seems to point to there being one (including engine analysis). Of course, Stockfish only pegs that advantage at around 0.3 pawns, and that advantage could easily be overcome by someone who is better at playing black.
I definitely don't get all of the complaints that a tendancy to draws is bad because players should have a 'fighting spirit'--whatever that's supposed to mean--or that a draw in under 20 moves isn't real chess. I could choose to play chess by setting up an extremely solid position and then just wait for my opponent to make a significant mistake.
As for draws preventing exciting chess, I think that most half-decent chess players would find it a joke if chess were hyped up for the person with an average IQ of 98 (US. The highest average IQ is 107 in Hong Kong). Just think of it like playing chess against a complete beginner--pins, forks, and general obvious attack plans would be all that the commentators would focus on. It would go like, "Oh, wow! Look! Carlsen has now put a fork on Nakamura's Knight and Pawn! After this, Carlsen will be up by 1 point in material and Nakamura will have to work hard to come back from this." or something. Obviously if chess were a national sport, everyone would know what forks and pins are, but chess is an intellectual game and so the natural audience will also be somewhat intellectual.

@ Zigwurst: do you think it would generate any serious amount of audience? IMO you need to understand chess at least a little bit, if not quite a bit or just a lot, to enjoy the way grandmasters play

Commentating futbol style! Anand defending R vs RB! Mastery in the defense. Reaction......oh Rb7! Genius? No, it drops piece! He takes! GOOOOOOOOL!

How about 0.4 for a draw with white and 0.6 for a draw with black....just a thought...
Another assumption that a draw with Black is somehow superior to a draw with White.

A fair assumption though -wether the 0.6 and 0.4 reflect the disadvantage/advantage is another matter. Karpov once said that he could almost guarantee a draw as white if he played in a particular fashion, but not as black...
I'm fine with the current system, but why not make black earn more points for a draw than white? For example, black could get 0.55 points and white could get 0.45. It'd increase the excitement among audience members who aren't good at math ("Who is winning overall?") and it might 'motivate' white to use their first-move advantage to win more. Yes, black would probably go for more drawish positions, but that seems to be the general trend anyways.
Or, we could just keep the current system.