1. d4 c5 2. d5 g6 3. c4 Bg7 4. Nc3 d6 5. e4 Nf6 6. Bf4 O-O 7. Qd2 Re8 8. Be2 e6 9. Nf3 exd5 10. exd5 a6 11. O-O Bg4 12. h3 Bxf3 13. Bxf3 Qc7 14. a4 Nbd7 15. Rfe1 Bf8 16. Ne4 Nxe4 17. Rxe4 Rxe4 18. Bxe4 Re8 19. Re1 Bg7 20. b3 Be5 21. Bxe5 Rxe5 22. Bf3 Qd8 23. Rxe5 Nxe5 24. Bd1 Qf6 25. f4 Nd7 26. Qe3 Kf8 27. Bg4 Nb6 28. a5 Na8 29. Bc8 Qa1+ 30. Kh2 Qxa5 31. Bxb7 Nc7 32. Bc6 Qa1 33. Qf3 h5 34. f5 Qe5+ 35. Qg3 gxf5 36. Qxe5 dxe5 37. d6 Ne6 38. Kg3 e4 39. Kf2 Nd4 40. Ba4 f4 41. b4 cxb4 42. c5 b3 43. Bxb3 Nxb3 44. c6 Ke8 0-1
There are a few points here that make it a bad idea.
First and foremost, white's dark squared bishop in this pawn structure is his good bishop (and it's extremely active). While black's fianchetto'd bishop is also good, it isn't directly influencing the position until the knight on f6 moves (which you'll notice never happens in this game until his opponent mis-steps and trades knights).
Secondly, trading the kingside fianchetto'd bishop is usually good because it leaves black with dark squared weaknesses that white might be able to take advantage of and attack. Notice how Simon Williams calls Qd2 "an aggressive plan." He's already envisioning white trading bishops, and going for a kingside attack. However, in this position, white does not really have any pieces aimed towards the kingside that he can use to attack black's king. And the possible plan of h4-h5 to open up black's king falls flat in the Benoni when black is able to quickly open the center of the board with e6-exd5. If black had already played e5, then it would be entirely different.
Lastly, notice that when the pieces start to get traded off, BLACK offers to trade this bishop for white's (41:20ish). The reason here is that the position has transformed largely into an endgame, and Simon Williams discusses how he wants to get the classic good knight vs bad bishop endgame. All of white's pawns are stuck on light squares, impeding his minor piece's mobility. Whereas black has a few important dark squares his knight can jump to in the center of the board where it influences everything (e5 and d4 in particular, possibly c5 if white plays b4 cxb4).
Usually the fianchetto'd bishop is strong because the h8-a1 diagonal has a lot of juicy targets it can aim at from a distance. In this game, the diagonal never really meant anything.