Point is, collectively losing whoever, is never lead anyone into joining the crew.
The present discussion is whether or not Carrot had substantial moments with the crew and more specifically Luffy, not if she'll join strictly because of it.
The problem is that in vagueness and arbitrariness of what it means to have a meaningful interaction with Luffy and the crew, people just roll with what they want. So when Carrot supporters point out that their friend Pedro died in front of everyone and that the SHs mourned together while Luffy left to fight Katakuri after reacting twice to Carrot (first after Katakuri stomped on her, then trusting her by name to protect the ship alongside the crew), Carrot deniers will just say that there's no weight to that scene. And if supporters make a slide show of all the interaction between Carrot and Luffy and how she was portrayed as a piece of the crew instead of a guest, it's also meaningless. There's no possibility of consensus.
Meanwhile, a character like Franky who played a HUGE role in Enies Lobby (therefore deserving of his recruitment) didn't have any meaningful interaction with Luffy before his joining except for their fight in Water 7, but let's forget that…