.....I doubt sponsors of any size give it any thought, at all.
Harold Duvall and the folks at Innova, among the more influential people in our sport, haven't given us a hanging basket, but they're certainly not averse to trying out unusual things in big events.
If we ever got to the point where we had real sponsors, putting in real money to advertise to real spectators, my guess is that they'd support the unusual and exciting.
In the meantime, the objections will come from purists and those who see hanging baskets as adding flukiness to the game. I would at least understand top pros, who have a lot riding on each putt, wanting baskets to be as uniform as possible, and that uniformity including the basket being stationary. It's why I don't think they're appropriate for Worlds and NTs.