I just thought about this scenario yesterday. It kinda makes sense for Carrot to join Blackbeard Pirates, no joking.
1. Carrot has been consistently portrayed as someone evil throughout Wano arc. It's just that she happens to be in protagonist's side so probably some people don't notice it.
She kept spreading the whole propaganda of "Perospero killed Pedro" and she made not only few, but lots from Mink tribe, including Duke Nekomamushi, believing her false words.
It's like Oda is trying to set up Carrot's dark nature, as a manipulative woman who can trick lots of people, including those stronger than her, to do the work for her.
By any chance if Blackbeard (who somehow already knew the whole story of Carrot, Pedro and Perospero) met her, he maybe like:
Blackbeard: I have seen the potential in you. I can see darkness deep beneath your heart. Pedro's dream shall never end! Join me!
Carrot: *unsures yet eventually agrees*
2. Powerlevel wise, Carrot will gain more by joining Blackbeard than joining Luffy.
By gaining Luffy, most likely she will only end up being grouped together with Chopper and Usopp, acting silly then cowardly. Without Sulong, she is Weakling Trio level.
And with Sulong, which apparently only happen once in a month, she levelled up to Nico Robin level? But then again I'm not actually sure she can match the demon Robin who defeated Black Maria.
But by joining Blackbeard, she can become a strong character quickly. Blackbeard will just hand her another overpowered devil fruit.
3. Carrot's opponent in SHP vs BB arc
It's Chopper and imo this will be a better fight than these Chopper vs Dr. Q / Stronger / San Juan Wolf predictions.
Because it is not only a random battle, but a battle with drama and emotion. "Once acted as close sibling in WCI arc, now the two meet again but as enemies".