Why must the point be shared 50-50?

Here is a whimsical suggestion: As the rules stand, two chess players can, by mutual consent, score the game as 1-0 or 0-1 if one player resigns or as .5-.5 if they agree to a draw. Why should other scores be forbidden if both players agree? At any stage of the game I should, on my turn, be allowed to offer my opponent .32 points in which case I get .68 points. After making the offer and hitting my clock, my opponent can accept or decline my offer or make a counter offer. E.g. "Give me .41 points and content yourself with .59 points and it's a deal.". Any thoughts on how this would work in practice if one ran a GM tournament with this rule?

No. Chess is about the battle between 2 minds, not to negotiate about points to reach a certain ranking in a list which would favor both.

Then why should they be allowed to agree to a draw rather than playing out the game?

VyboR wrote:

No. Chess is about the battle between 2 minds, not to negotiate about points to reach a certain ranking in a list which would favor both.

Not applicable.

"If they think that both of them can't win the game, they can agree to a draw rather than playing it out."

I disagree.  If you think you can't win the game, then that leaves the option for a loss.  The original poster has a valid point, but it needs to be dealt with according to the rules of law, coleslaw, and without flaw. 

Read on McDuff.

"After making the offer and hitting my clock, my opponent can accept or decline my offer or make a counter offer. E.g. "Give me .41 points and content yourself with .59 points and it's a deal.". Any thoughts on how this would work in practice if one ran a GM tournament with this rule?"

Ok, so if you have checkmate in 1 can we stop there and you get .99?  This is where your logic meets a zugzwang end Neil Armstrong.  One step for man is not one step for mankind on the chessboard homeyo skillet.

Rules have to be in place, and we must abide by the rules of law, coleslaw, and without flaw. 

Computer engines should be used to determine the end result.  For example, my Russian vodka bro drew with my Indian curry bro.

[Event "3rd Norway Chess 2015"]
[Site "Stavanger NOR"]
[Date "2015.06.18"]
[Round "3.5"]
[White "Anand, Viswanathan"]
[Black "Grischuk, Alexander"]
[Result "1/2-1/2"]
[ECO "B33"]
[WhiteElo "2804"]
[BlackElo "2781"]
[PlyCount "81"]
[EventDate "2015.06.16"]
[SourceDate "2015.02.07"]

1. e4 c5 2. Nf3 Nc6 3. d4 cxd4 4. Nxd4 Nf6 5. Nc3 e5 6. Ndb5 d6 7. Bg5 a6 8.
Na3 b5 9. Nd5 Be7 10. Bxf6 Bxf6 11. c3 Bg5 12. Nc2 Rb8 13. a4 bxa4 14. Ncb4
Nxb4 15. cxb4 O-O 16. Rxa4 a5 17. h4 Bh6 18. b5 Bd7 19. Nc3 d5 20. exd5 Kh8 21.
Be2 f5 22. g3 Qb6 23. O-O Rbd8 24. Kg2 Bc8 25. f4 Rfe8 26. fxe5 Rxe5 27. Qd4
Qf6 28. Rc4 Bd7 29. Rf3 Bxb5 30. Nxb5 Rxe2+ 31. Kh3 Rxb2 32. Rc6 Qxd4 33. Nxd4
Rd2 34. Ne6 Re8 35. Rxf5 g6 36. Rf6 Kg8 37. d6 Bg7 38. Nxg7 Kxg7 39. Rf4 Kg8
40. Rc7 Rxd6 41. Rff7 1/2-1/2

The obvious mofo Stockfish ramifications of the upper atmosphere olympic 1-10 card raise tells us clearly only 8% is in contention.  With a 23% hombre start for white, Tonto is telling me that is a 15% loss yo we yo!!!

I am no Harvard grad, but the armpits are telling me that ain't good.

In that case, following your proposal, Anand would lose 8% making it .42 for him and .58 for Grischuk.

All facts and data collected are property of the Gonzo Corporation. 

"oops I've gone gonzo, have you?"

The simple answer: it complicates things. At the moment, all points in chess are in halves (one half for a draw, two halves = 1 for a win, etc); with your suggestion, who knows how the points will be. In cents (68 cents vs 32 cents for .68 to .32)? Millipoints (680 millipoints vs 320 millipoints)? What if you say "you'll score pi-3 points, and I score the rest"? What about even more stupid numbers?

Second, if the offer is not 1-0, .5-.5, or 0-1, then one of the parties will always be better off rejecting (or not making) the offer. Suppose the .68 vs .32 thing. If you think you'll be winning, you should reject it to aim for the win. If otherwise, then the opponent will score at least a draw, and thus your opponent shouldn't have made the offer.

Of course, the way out is to make results of chess to worth different points; for example, stalemate gives .7 to stalemating, .3 to stalemated; threefold repetition gives .4 to claimer, .6 to opponent; etc. But this, again, complicates chess without adding much to the core game.

I played a game once and it was quite drawish, but I was ever so slightly better, so I asked my opponent if he was willing to accept .4937602575894152 of a  point. He said he would, so I pocketed the .5062397424105848. I was quite happy with that outcome.