I totally agree - toxic behaviour, even when not bullying saps energy, morale and instills fear at times. The impact of organisational productivity and your top performers is potentially massive. But unless you have actual clear cut examples, evidenced, and of a direct impact on your personally in a way that explicitly contravenes the bullying policy / code of conduct it's impossible to take it further.
Even when you do have concrete evidence of bullying (and not just a "he said she said" situation) the worst case is usually a warning for the individual and they just learn to be more covert and cover their tracks better going forward. You still have to work with them, and usually whilst they might turn over a new leaf for a few months afterwards, a leopard doesn't change its spots. They just get cleverer about it and more subtle. And you would be surprised just how weak witnesses are in conveniently "not remembering" what happened as they son't want to get heat from the bully themselves.