There is an issue though, he has a crew and joining the SH's directly would mean relinquishing his crew. If he wanted to do that why wouldn't he have abandoned them for Ace, WB or BM by now?
Why would he? How do you even know he had an invitation to join these crews?
And you could say he could join and let the Sun Pirates operate under a new leader under the SH fleet but when has Luffy hinted he'd be ok with Jinbei separating from his crew to ride on the Sunny?
Oh man are we really saying this argument
still? Luffy doesn't give a shit if someone separates from their crew to join his so long as the crew is okay with it.
Luffy took Sanji from the Baratie.
He took Franky from the Franky Family.
He keeps on saying that Law is a Strawhat, even though he knows Law has a crew of his own.
If the Sun Pirates said they're cool with it, then Luffy wouldn't give a shit.