Personally, I think Carrot has been handled well.
I think it's important to remember that many of the expectations for new crew members are fan-imposed.
I'm just looking at it in really simple terms. Pedro accompanied the crew on an adventure to rescue Sanji. Initially this is framed in the context that Pedro is simply repaying the debt he owes Sanji for helping to save Zou from Jack and the Beast Pirates. Of course we later learn that Pedro has a tragic backstory and a personal history with Big Mom. Having lost most of his lifespan, he's a man living on borrowed time. We learn that he once met Roger and dreamed of sailing with the former Pirate King. He was told, being too young to sail at the time, that he would one day have his moment to shine. Pedro had all the traditional makings of a Straw Hat. He had a unique quirk, an epitaph, a bounty, a tragic backstory, and a dream. He was perfectly set up to join Luffy and crew for the duration of their adventures if not for the fact that Linlin stole his lifespan, in a manner highly reminiscent of Moria robbing Brook of his shadow. In the first half of the story, in Paradise, Luffy would beat up the big bad villain and force them to restore Pedro's missing years, allowing him to take his place among the crew.
But that's not what happened. Linlin is another level of opponent and survival was the best the Straw Hats could hope for and survival came at a tremendous cost - Pedro's life was sacrificed for them to continue living.
But that's not the whole story. Carrot enters the picture. A naive stowaway excited by the idea of adventure, naive to the dangers of the sea. She accompanies the crew on their first foray into the heart of an Emperor's territory. At the outset of their voyage she exclaims her enthusiasm for the romance of adventure which would not at all be unfamiliar in the early arcs of One Piece. She's immediately awestruck by the sheer scale of the ocean and the world beyond Zou. She immediately meshes seamlessly with the crew, but ultimately plays the role of companion to Chopper in his mirror world adventures for the first half of Zou. Worth noting is that Carrot is ultimately responsible for Brulee's defeat, which serves a pretty crucial role in the crew's antics for the duration of the arc.
Everything changes at the moment of Pedro's death. Carrot is confronted with the harsh reality of an adventure at sea. Her mentor, the one who gifted her with the cape and claws she adorns on Zou, dies to save her and the rest of the Straw Hats. Pedro imparts to Carrot his belief that the Straw Hats are going to fulfill a prophecy long held dear by the Minks and people of Wano and implores her to help fulfill his wish that the Straw Hats bring about the 'New Dawn.'
Luffy enters the mirror world to face Katakuri and, before departing, gives a command to Carrot, Jimbei, Nami, Chopper, and Brook as equal members of his crew. Carrot is instrumental in the defense of the Sunny against an Emperor of the Sea. She turns her feelings of loss and despair at Pedro's death into motivation to guard the Straw Hats, uses Sulong at a crucial moment, and when all is said and done provides a moment of catharsis for Sanji at the conclusion of the arc.
Carrot goes through a full character arc over the course of Whole Cake Island. At the outset of the voyage she is naive and unaware of the dangers of the voyage that lies ahead. By the end of the arc she has suffered the loss of a mentor and been entrusted with carrying on his will into the future. She is able to both mourn Pedro's loss while also providing comfort to Sanji in a cathartic moment where they share in the memory of who Pedro was and what he stood for.
Carrot has undergone a transformation. She's not the same person she was on Zou. She understands danger and loss in a way she could not before. She has motive to accompany the Straw Hats on their adventures beyond a naive and childlike desire to see and experience the world beyond the borders of her safe and familiar home. She proved invaluable in an arc where the Straw Hats faced their greatest enemy to date.
Now that the crew is again facing Big Mom and Kaido, Carrot is standing right alongside them aboard their ship. It can be argued that the 'New Dawn' is a yet unexplored idea, but I hardly think it is as nebulous as some are claiming. The New Dawn is largely understood to be the series endgame - the conclusion to the final war that follows the discovery of One Piece. The symbolism is pretty clear to my mind. The concept of bringing about 'The New Dawn', implies the world is in a state of symbolic 'night'. It implies a restoration of the natural order and the ushering in of a new era. Of course the specific details of 'The New Dawn' will not be fully illuminated until the end of the series when these events inevitably come to pass. That does not invalidate the desire to see that the Straw Hats are successful in this quest as a motivating desire for Carrot in any way. In fact, I'd say it's not substantially different from other members of the crew whose goals are similarly intangible. Robin joined as the crew archaeologist in search of the True History. When she set out on this quest for knowledge she knew little of what she would ultimately discover and when she joined the Straw Hats the readers knew little of the fruits of her labors to that point. We still know nothing about the All Blue, the ultimate goal of Sanji's quest. We don't know what goal post will allow Usopp to be declared a 'brave warrior of the sea' or Chopper to be declared a 'great doctor capable of curing any ailment.' We don't know why a full map of the world doesn't exist. Most significantly, we still don't know what One Piece itself is or what its discovery means for the world. Importantly, we knew less, almost nothing, about these end goals when the characters in search of them first joined the Straw Hats. The characters themselves knew almost nothing about the true nature of the dreams they set out in sea to realize at the outset. That's the thing about a journey - you don't really understand the treasure you seek at the outset of the voyage and most certainly that which you find will differ wildly from that which you expect. Carrot doesn't know what 'The New Dawn' means yet and neither do the readers. It's something we'll discover together. When Luffy set out in the first chapter, we didn't know what One Piece was, where it was located, how it could be discovered, or if it existed at all. We've slowly learned those things over the course of almost 1000 chapters and are still left in the dark. It's important to take a cue from Luffy here in understanding the nature of adventure. When given the opportunity, Luffy didn't even want confirmation that the treasure exists, much less to know what it is or where it's located. Discovery is the great joy of adventure.