There was an old thread about why top players didn't play the Dutch. Currently the Leningrad is played a bit but I still wonder what the problem is with the Stonewall.

As far as I can tell, there is no easy way even to a slight advantage for white. For example, against Avrukh's repertoire there is a least two ways to at least equalize. One way was shown by Gleizerov:
 
[Event "It (open)"]
[Site "Vienna (Austria)"]
[Date "2011.08.19"]
[Round "7"]
[White "Klocker Benedikt (AUT)"]
[Black "Gleizerov Evgeny (RUS)"]
[Result "0-1"]
[Annotator ""]
[BlackElo "2590"]
[Classes "0"]
[ECO "A90"]
[GameID "0"]
[Remark ""]
[Source ""]
[WhiteElo "2218"]

1. d4 e6 2. c4 f5 3. g3 Nf6 4. Bg2 c6 5. Nf3 d5 6. O-O Bd6 7. Nc3 O-O 8. Qc2
Bd7 9. Rb1 Be8 10. b4 dxc4 11. b5 a6! 12. bxa6 Nxa6 13. Rxb7 Qc8 14. Rb2 Nd5
15. Nb1 c3 16. Nxc3 Nab4 17. Qd2 Nxc3 18. Qxc3 Nxa2 19. Qc4 Nxc1 20. Rc2 Ba3
21. Ne5 Rf6 22. Qc3 Qa6 23. Nc4 Bh5 24. f3 Rff8 25. Qe3 c5 26. dxc5 f4 27.
Qxa3 Nxe2+ 28. Rxe2 Qxc4 29. Qb2 fxg3 30. hxg3 Qxc5+ 31. Kh2 Bf7 32. Qe5 Qb6
33. Rb2 Qd8 34. f4 Ra5 35. Rb5 Ra2 36. Rb2 Ra3 37. Rf3 Ra5 38. Rb5 Rxb5 39.
Qxb5 Qf6 40. Qe5 Rc8 41. Ra3 Qxe5 42. fxe5 h5 43. Ra8 Rxa8 44. Bxa8 g5 45. Kg2
Kg7 46. Kf3 Bg6 47. Ke3 Bf5 48. Bf3 Kg6 49. Be2 Bc2 50. Kd4 g4 51. Bb5 Kg5 52.
Bc4 0-1
 
It is perhaps the opening that grabs most space vs 1. d4 and black normally has a lot of chances as well, which should fit a player like Carlsen. Is there even an "easy" draw for white?

The only thing I can think of is the Nh3 variation, but AFAIK it can be handled by delaying d5, avoiding some critical variations.