Simple simple simple question. As per all shonen series, power levels do help dictate screen time. They're not the only thing to go off of, but generally speaking, you get boosted by them. You always have your exceptions like Nami & Usopp, but they've been in the crew since the start.
So, the simple question of it, if Carrot was as strong as someone like Nico Robin or even Sanji, would that help her odds of getting into the crew? She'd have more screen time and generally be doing more things and being seen as a reliable ally. Because Yamato is getting a ton of screen time and has solid chances of joining the crew too and I can't help but think the fact she's top 5 in Onigashima right now is helping out why she's getting so much screen time. She can do so much to effect the plot, whereas Carrot currently can't.
Or, does it not really matter? Is she doomed to be a side character forever and be forgotten after Wano?