1- It is not this version of Brook that will defeat a TR. Current Brook is stronger than its WCI version and will still receive a great power-up to do so.
2- We do not know the conditions that Perosperos arrested them. Perosperos managed to arrest the entire vinsmokes family in an instant when they were off guard. Peros may have caught them off guard when they fought with the randons.
3- The fruit of Peros is quite hax. Caesar also knocked Luffy out with hax, this does not necessarily explain the level of power.
4- Brook and Chopper were already exhausted fighting other opponents
5- Katakuri was there, so he may have interfered
2- We do not know the conditions that Perosperos arrested them. Perosperos managed to arrest the entire vinsmokes family in an instant when they were off guard. Peros may have caught them off guard when they fought with the randons.
3- The fruit of Peros is quite hax. Caesar also knocked Luffy out with hax, this does not necessarily explain the level of power.
4- Brook and Chopper were already exhausted fighting other opponents
5- Katakuri was there, so he may have interfered
