Next to the fact that the whole story leads more and more to an obvious final war arc against the WG (Imu, God knights, Seraphims, Uranus usage, Flood plot, Lore drops, Joyboy call outs, the treasure being a useable thing, Luffy's true dream...), it's easy to explain why the Strawhats are not invested into the world saving-plot yet:
Their reality is still heavily centered around the PK race, even though the story started to break away from that. They are not yet actively involved in the anti- WG/World-saving plot. It's really just that.
That will change a lot, when the water levels will start to rise more and more and they will notice themselves and when they get into possible exchanges with factions, who are heavily mentally involved in that plot and/or have knowledge of the greater lore: Shanks, Sabo, Vivi, Kuzan, Sword members, Elbaf giants, Saul...
The Strawhats' interest and involvement will then start to grow and it will peak on Raftel, when they get to know the true history and get their hands on the treasure, that's likely even needed for the grand finale.
Need to keep in mind that Joyboy vs Imu, World's freedom vs oppression, back to one continent vs further flooding, Red Line vs no Red line etc. all heavily bolstered by future, major lore drops is thematically outshining every opposing ideals and themes you can come up with for a Luffy vs Blackbeard fight.
Add that the Anti-WG plot within the Marines still has not even started yet officially. Akainu even seemed to know what VP was talking about. And the Sword agenda plot still has to evolve much further. Right now they have not infiltrated or betrayed anything or anyone.
Thus the WG still seems safe from internal conflict and therefore also won't get seriously threatened anytime soon.
Imo most of their manpower will still remain after the PK race. They have Imu, 5 Gorosei, 7 Seraphims, 9(+) God knights, Uranus and still the support of the Marines. Not one of the other major factions alone can do shit to them, so it first and foremost has to come to a point, where a massive union gets formed, that actively wants their asses.
That's not happening, when BB is in to take the spotlight next and the One Piece wasn't even found yet.