Staff now recommend completely removing the swing, and Bainbridge said if injuries to any other council-owned equipment were reported it would be disabled immediately.
A safe landing area for people jumping off the swing cannot be guaranteed, she said.
Councillors Rob Vinsen and Alan Taylor were keen for the removal.
Vinsen said one person had shattered both heels and ended up with both legs in plaster.
The risk was unacceptable, he said.
Taylor said the council had abrogated its responsibility to officers by putting the swing up and councillors should "walk away with egg on our faces".
But other councillors had no appetite to remove the swing.
Josh Chandulal-Mackay said if the motion to remove it had succeeded he would have asked for another swing, somewhere else.
Jenny Duncan said the council shouldn't remove all thrill and excitement, and Mayor Hamish McDouall has talked to German tourists "buzzing" about it.
Charlie Anderson suggested consulting the Watson family, who put up the first swing, which was attached to a poplar tree.
They decided to ask council officers to look for a way to modify the swing's design to make it safer, up to a total cost of $25,000, and also get advice on legal liability for people hurt while using it.
Vinsen and Taylor voted against this.
.