@Gear-4-Sauce This is my take on the matter as well. The current situation feels more like a false positive: it looks like victory has been achieved, but due to previously established factors that the Straw Hats haven't addressed or didn't overcome they're about to hit some sort of a wall.
We can already see parts of that in play. The Seraphim are contained, but the orders York gave them evidently haven't been overridden. The other CP agents have been fed but not freed, and Oda took a moment to remind us that York wanted them to remain unharmed for reasons currently unknown. The other satellites have been given important tasks to enable their escape, but the previous history calls into question on whether or not they'll be able to follow through on those tasks. The Frontier Dome is keeping them all stuck, but also feels like the only thing preventing the crew from getting immediately swarmed so the room for error is small... and the percentage counter for the Frontier Dome would make for a mighty fine ticking clock. We know Blackbeard wants his island to be made an official kingdom, that a Blackbeard ship is somewhere on Egghead, and that one of the BB Pirates we have yet to see this arc - Laffitte - is the one who talked the WG into making BB a warlord the first time around; even if it isn't the missing BB pirates on Egghead, the rest are connected to the subplots involving Law and Garp. We haven't even seen Caribou since he got kicked off the Sunny and swore he'd get back at them.
There's a lot of failure points in the escape plan despite York's capture, and I personally didn't feel like it deflated what she brought to the table. By 1079 I felt it was clear that she was going to be a secondary antagonist given that she admitted that she wouldn't win in a straight fight, and the additional information in 1089 further characterized (or rather I should say confirmed) her as the kind of secondary antagonist similar to Spandam or Helmeppo - particularly that her biggest character flaw is that she's short-sighted and overestimates her superiors' ability to be reasonable. So just because she's caught now doesn't mean she can't cause problems later.
@King-Cannon said in Official Egghead Thread:
A lot of the cutaways were significant because some elements needed to be introduced in other subplots before Oda could proceed with Egghead's plot, the Mother Flame being the first that comes to mind.
I think the big thing I'm not 100% clear on when it comes to the cutaways is the arrangement.
Typically when cutting between subplots, the beginning of one scene will in some way answer a question raised at the end of the previous scene - the most obvious example I can think of this is a show like Archer where the scene transitions are tied together by having dialogue at the start of a new scene picking up where the scene before it left off. With the Egghead arc some of these types of transitions/connections are obvious - the match-cut of sorts that happens between a Pacifista causing an explosion on Egghead and an explosion in the fight between Law and Blackbeard, York saying that the world only needs one Vegapunk being immediately followed up with a panel of York complaining that the WG wants to kill all the Vegapunks, the Blackbeard ship reaching Egghead being followed up with Shanks and Kidd clashing having the connection of the last remaining Emperors of the previous generation crossing paths with the new/worst generation, etc. - but the reason for the placement of other scenes still remain unclear to me. For instance, I'm still not quite sure what the connection is between Law's defeat being succeeded by a sequence of Sengoku and Tsuru talking about the death of T-Bone and the Cross Guild, nor what Myosgard's execution has to do with Garp punching battleships and mentoring Kuzan.
While the reason for the sequence of events could certainly become evident later down the line, I think that's the biggest reason the cutaways might've felt jarring to some.