The Kage Summit happened because of Sasuke's attack on Killer Bee. That was what pushed things to the tipping point between the villages, particularly considering Konoha's previous neglect to really deal with Sasuke.
Danzou was in power because Konoha was weakened by Pain's previous attack on the village; this happened because Itachi was dead (after his battle with Sasuke), which basically allowed Akatsuki to attack the village sooner than expected. This invasion also marked the culmination of the "Akatsuki" arc, where the leader showed himself in a full-scale attack, and the villages could no longer pretend the organization was something they could handle on their own.
Danzou was obviously deeply connected to Sasuke's character arc; he ordered the Uchiha Massacre, knew Itachi's identity, and had ordered a member of Root (Sai) to assassinate Sasuke (behind Tsunade's back). So it was fitting that, in an arc basically focusing on Sasuke's descent into darkness, Danzou would be present. And since Sasuke's hatred stemmed from Konoha's darkness, it's fitting that Danzou would be the main villain. A confrontation with Danzou was clearly the "next step" for Sasuke.
The fact is, Danzou seized upon Tsunade's absence to further his ambitions; it's one of the reasons he allowed Pain to do so much damage, and didn't send Root to aid (or help out, himself). So it's not a total "plot convenience" or "coincidence" that all of this happened while Tsunade was out of commission; much of that was Danzou's fault, and the rest happened as a result of Sasuke's actions.
I agree the arc was poorly-written; however, the basic Sasuke vs. Danzou theme throughout the arc is not to blame. Killer Bee vs. Kisame was a really random filler battle, and kinda sucked. The Ao vs. Fuu/Torune, and Tobi vs. Fuu/Torune, were also terrible. Basically, it was the filler action.
Sakura's confession was probably Sakura's lowest point in the series, and IMO was a major reason why Kishi decided to cut her screen time to almost nothing throughout the majority of the War Arc.
Naruto's hyperventilation / fainting spell was, likewise, probably Naruto's lowest point in the series. He, however, redeemed himself at the arc's conclusion when he finally met Sasuke. Sakura merely came off as being a weak failure when she backstabbed her comrades to attack Sasuke, then failed to kill Sasuke, and then cried and relied on Naruto once again.
I could go on; my main point is that I believe the Danzou / Sasuke "coincidences" complained of in the OP are not really that contrived, and fit squarely with Sasuke's development in that arc. The main problem in that arc was pacing, which was bogged down by these other, horribly-written sideplots. If the Naruto/Sakura portions of the arc had been better-written, and had complimented the rest of the arc rather than detracted from it, I believe the arc would have been fine. Instead, I find it to be a fairly forgettable arc, and Sasuke's development did a 180 pretty quickly in the War Arc (as did Sakura's when she was finally allowed to become semi-relevant again nearly 16 volumes after the Danzou arc).
