The idea of a bike path at chambers is ridiculous. It's like riding on rocks on chambers and on top of all that, it's always packed with cars and people. People jay walk on chambers so much because there's so much traffic, it takes cars forever to move.
Anyway, I only ride through that 10 second path at night where there's only a few people. They did add an extra sign for bikes to dismount. I usually dismount if there's a lot of people but I do see people refusing to simply dismount and instead squeezing through crowds like asshats.
I just stumbled upon it last summer even though I live less than a 10 minute ride from there. Instead, I had been taking the Lafayette Street bike lane and dealing with that odd transition in Foley Square that leaves cyclists hugging the center line in the middle of the intersection at Chambers Street.
I hung around one day, photographing people playing the piano that was there as part of the "Play Me I'm Yours" project. I guess the City didn't feel it was so busy that they couldn't place a piano in that spot and, despite the fact that it was a beautiful afternoon in the middle of summer when the path was fairly busy I didn't notice any bike pedestrian conflicts. Everyone seemed quite courteous and was respectfully sharing the space.
If pedestrians feel it's unsafe then maybe they should consider using one of the other, pedestrian exclusive, routes through the park.