Well, actually, the Strawhats probably DO need to get to Hachinosu at some point. Becaue Hachinosu has one of the Rio/Historical Poneglyphs that Robin needs to find in order to learn about the Void History.
The 4 Road Poneglyphs are the ones that get all the attention. Because they're flashy and red, and lead you to the big treasure at the end of the story. But, the Rio Poneglyphs are probably just as, if not more, important, since they give you a full telling of what happened during the Void Century.
There's 9 of these Rio Poneglyphs, and the Strawhats have had access to information on 8 of them. The ones from Ohara, Alabasta, Skypiea, the 2 on Whole Cake, the 2 on Wano, and the one on Egghead (either from reading Vegapunk's notes about it during the Missing Night or just asking Lilith about it). The one that's on Hachinosu that Blackbeard conquered the island to get access to is the only one the Strawhats still need Robin to see. Robin's actually been pretty dutiful about collecting all these Rio Poneglyphs in the background of the story for decades now. The girl knows how to prioritize important side quests that get you a Secret Ending.
Artur made a pretty good breakdown of all of this pretty recently here:
So, unless Blackbeard takes the Poneglyph with him somewhere else, the Strawhats might need to go to Hachinosu.
Although, I suppose if Pudding escapes from Blackbeard then SHE can tell Robin what the last Rio Poneglph said.
So, either the Strawhats need to get to Hachinosu or they need to rescue Pudding. One way or another.
As for rescuing Garp....I'm not sure if Luffy would actually be worried about Garp getting captured or not. Luffy knows how tough Garp is and would probably assume it's all a trick he's pulling on Blackbeard. "Oh...Gramps is gonna be so mad when he wakes up. Those poor pirates..."
Going to Hachinosu WOULD give us a excuse to see Gin and Don Kreig again, though. So...yeah, I could see us going to Hachinosu. It'd make for a fun fight arc. I've speculated before that Blackbeard might be interested in stealing Elbaph's Legendary Devil Fruit for himself. So, a Hachinosu arc might end up being a natural sequel to Elbaph, in some ways.