"AP doesn't matter, Sougo doesn't have Acausality so Alvis can easily meddle with his past before he gained 2-B powers and thus prevent him from gaining the powers and resistances of even Zi-O II and then incap him."
Yeahh, no.
First of all, one of Oma Zi-O's powers is to literally destroy and recreate Space-Times so he can and will undo Alvis' meddling.
Second of all, it doesn't work like that. The first and last time Oma Zi-O was retconned was when he willingly allowed his younger self to do so. When Another Zi-O II changed the timeline by erasing and making it so Sougo would never be Oma Zi-O (Because he would've died), Oma Zi-O in the future was unaffected but was more worried that his entire world would be erased and paradoxes.
As for "No resistance against Precognition", no he blatantly does.
Another Zi-O II has precognition and tried to use it on the Weaker GrandZi-O and he saw that GrandZi-O died against him, which only resulted in Another Zi-O II getting smacked in the face because Precognition simply doesn't work on Sougo anymore.
And AGAIN, it's not even like Time Paradoxing will keep Sougo down WHATSOEVER. Kamen Riders will always exist as long as someone remembers them- and there is flat out a Singularity Point (Acausal Type 1) that remembers Sougo. It's a plot point in the Build/Zi-O Crossover movie that the villain is retroactively trying to make Kamen Rider never exist but that damn one kid is keeping literally everyone's existence... existing.
Furthermore, the creation of an Another Rider is literally Time Paradoxing your powers away. If an Another Rider exists, you will effectively have never been a Kamen Rider since your history as a Rider went over to another person. Great example is the moment when Another Ghost was defeated, the actual Ghost literal right that moment got his memories and powers back because his history literally returned.
And yet here we are, with Zi-O fighting Another Zi-O completely fine.