Lots of great reasons why Carrot doesn't follow the typical Strawhat template. However you look at Rogers and Whitebeards crews and they had places for young hanger-ons who weren't powerful or even useful really. What point did Shanks really serve on Rogers crew? I can see a spot/purpose for Mononosuke but Carrot no. Luffy is still young and his ascent is relatively fastpaced (in manga timeline) so he's not really going to find space for a deckhand. Carrot would be the perfect candidate for that.
I can see Luffy never formally asking Carrot to join the crew but every time they try to leave her on an island she stowsaway on the ship again until she ends up at One Piece with them all
Whitebeard really doesn't have hanger ons on his ship, Cat and Dog were retainers to Oden and left to follow Oden when he jumped ship and just by there appearance they were older then Shanks and Buggy, he also had no females on his main ship. Subordinate Captains are all old and experienced pirates from the NW.
Shanks and Buggy were both cabin boys/apprentice pirates on Roger ship but they were recruited way earlier even before Roger final journey to the NW and become PK and there skirmishes with WB and Garp. If they were gonna have cabin boys and such Momo and Chimney make more sense than Carrot.
I don't see any hanger ons staying for beyond the point of finishing whatever story ties they have (Kimemon and Law), I see Carrot being gone and on the alliance once Kaido is taken down.
Ssnji is on no team at this moment
First typo and second he is on a team, its Team L.