Carrot joining would be unlike anything that has ever happened before. Every SH had an arc where they was a main focus. Even Fishman Island focused a lot on Jinbe.
Carrot has been around for over 200 chapters and nothing. Yamato has been around less than 40 and already got a ton of focus.
There's also that Carrot was happy in Zou. Everyone loved her and the instant she feels put of place, they accommodate her like the other minks. All of the SHs struggled a lot and were pitiful for the most part in their past.
I definitely agree that the lack of a focused arc is what's killing Carrot right now. She needs one to join. I think there is still a small chance for it though.
Big Mom will likely not go down for good in this arc. The only chance for that is if she is straight up killed, which seems very unlikely. There are a lot of BM pirates who have been set up but haven't done anything yet, including two sweet commanders. There's also no chance they won't continue to go after Luffy after Wano, since they won't accept a loss when only two of them are there and Luffy had tons of allies. They'll blame it on the beast pirates being incompetent and the Strawhats having help.
Furthermore, Luffy declared that he would defeat Big Mom 3 times. First he said it to her on Fishman Island, then he said it to Kata on WCI when he vowed to come back for BM after he finished Kaido, then again in Wano when he arrives at the live floor. He absolutely has to be the one to finish her, not Law and Kid. Assuming there will be another Big Mom arc, presumably Elbaf, there's more opportunity for Carrot growth.
There's too much setup for Carrot vs Perospero for her not to beat him in the end. Where he told her she's not strong enough and she should go back to Zou to eat grass. Never does a One Piece character not turn the tables and win after a taunt like that, but it looks like Neko is getting involved instead.
Basically what I think is the last chance for Carrot to join is if the Perospero plotline isn't resolved in Wano and Carrot asks to tag along with the crew to continue to chase after Peros. Presumably then the final Big Mom arc would focus on Carrot.
That's a lot of big ifs and maybes, and I don't know if Oda would slow down the story to focus on Carrot if he really wants to end in 5 years, but I think it's a possible direction the story could take. Is it likely? Probably not. But that could be how Carrot is made relevant enough to join.
Regardless, I assume Yamato will join. Carrot would join in addition to her, not instead of her.