I am taking out my thoughts here.
Since, the alliance is formed between Kaido and BM, everyone thinks (including myself) that navy will definitely take part in war to level the playing field.
And, to be fair it's reasonable assumption.
However, I was asking myself a question why navy shouldn't take part in the war and I come up with some arguments and seek some discussion on them
1)Navy is unaware of their official declaration of alliance. All they know is BM will try to approach Kaido and is seeking alliance but not the official declaration.
Also, I doubt Kaido and BM would declare this to the world before fire fest as they both seem to be engaged in enjoying the feast for the festival with no anticipation of any threat.
2)wano forces remain unknown to navy. This is the reason Akainu stopped Kizaru from interfering. I doubt that suddenly navy would be able to know wano strength
3)Reverie just got over and considering how much chaos was due to happen in Reverie, I doubt navy would be able to free itself from Reverie aftermath to go against the alliance in just 5 days to fire festival.
4)one of the reason people think navy would involve is it justifies Kaido statement of 'greatest war this world ever seen'.
But point is, Kaido isn't preparing itself for greatest war at fire festival. Nor, as of now Oda has laid the build up to navy preparing for such war like he did in MF. I doubt Oda will suddenly bring navy into the war.
Your points are reasonable tbh.
Bt i think the meeting where Orochii fired at one of the Cp0 members could actually come bite back his ass. At one side this might appear to be something that simply is to hype up KAIDOU, making him such a beast that with someone like him by his side even Orochii can act in such way and Cp0 don't want to anger bt it also felt like Orochii was also testing CP0 temper there by doing things as he pleases and this plot point could grow into CP0 taking benefit of the situation.
As for Marine not being aware of Kaidou-BM Alliance? I think an alliance is one of the first few things that comes to Mind when Two Yonkou meet like it happened when WB n Shanks met(Gorosie discussing it) and same this time with Garp already commenting on it.
Anyway last we saw Akainu, he was stopping Kizaru because of not being aware of the strength of Wano Samurai, that imo could led to two situations. Either he plans on sending bigger force(regardless being aware of Kaidou-BM alliance) to Wano than before(because of uncertainty) or use spies or underworld network to find more about Wano, Akainu also dont mind using underhanded means for justice. Also who knows maybe there are already spies in Wano, if i have to name someone two names comes to my mind... Drake or Apoo. Drake is a former Marine who now seems to have his own scheme/agenda running on by going against Kaidou n freeing Law(atleast that us what Law word suggests). So mayhe he is still with the Marines and only freed Law for takin down DOFFY.
As for Apoo if he can betray once, he can do again.
If there are Spies Marine can get aware of the Alliance. Kaidou forces, Wano forces everything they want to know. Else the threat of alliance i feel is also good enough to take close eye on it.
I also questions why Oda delayed the fire festival so much, i mean we still have 5 days remaining even tho most of the necessary prep is done, or arguably Oda could have finished the prep early on if wanted to bt he delayed the battle more than a week, what if the reason behind this is so the Marine(atleast the Admirals) can wrap up Reverie and come to Wano. I think the Fire festival day being a Full Moon day could also be another specific reason.
As for Kaidou hyping up thr final war and Fire festival not being it. I think the major reason people were hyped is because of Editors statements that Wano final battle will even surpass MF. Tho fans had doubts about it at the start and only considered it as hyped statement like editors usually make bt given we saw Kaidou n BM alliance last chapter, that also seems to more n more true lately. Also it might not be the final war Kaidou talked about but all his forces seems to attending the Fire festival with Numbers also arriving in to join the festival.
And The Alliance taking down Two Yonkou at the same time also seems impossible so some external force have to halt one of the Yonkou, and Marines Admirals seems better pick here given Akainu also already talked about it and two yonkou meeting threatens the stability of the seas which Marine can't let happen so easily.