Jinbei didn't really have an arc. I got berated once here, because suposedly it was an iron clad deal that SH candidates all need Luffy to save them from someone in an arc to become nakama.
And somehow that fish villain (cba to google him) was Jimbei's arc villain because Jimbei couldn't defeat him himself.
Fishman island is when Jimbei "joined" but he didn't go with the SH, he went to BM to ask for his release.
In a way it's much more accurate to say the big baddie stopping Jimbei from joining was Big Mom, but Luffy didn't even save Jimbei from that, they just all collectively still decided to tag together.
And EVEN still that wasn't the arc where he officially joined, it was later on, randomly, in Onigashima. So this idea, that SH candidates need a big villain for Luffy to save them from is kinda of a meme, because it's jsut people looking into Oda's formulaic story telling.
Fck i'd argue not even Robin had that treatment, because Spandam was her personal villain (his dad killed Clover-sensei etc) and her biggest "villain" was her innability to not ask help and acept the SH as nakama at the start of Water 7.
Aokiji even stated Robin could have ran from CP9 if she wanted to, but she decided to suicide for the SHs.
So basically, you just need to have a role/dream and some arc importance to be a decent candidate imo