Once the Akatsuki sealed the Eight-Tails, barring any surprises, the final war would begin. Yan didn't believe Black Zetsu and Obito could resist making a move against a Nagato barely clinging to life.
Given Obito's current situation, he probably couldn't wait to crush Nagato to death, seize the Rinnegan, and take the field himself.
With only one Kamui Sharingan, Obito couldn't even get a chance to appear.
It wasn't that Obito didn't dare show himself. He was worried that once he did, Yan would get a hold on him. Kamui was undeniably powerful, but it also had its weaknesses. Once someone knew those weaknesses, targeting Obito became far too easy.
On top of that, Yan had his other Sharingan. If Yan wanted to keep him in check, it would be effortless.
That was why Obito refused to appear before Yan. After his identity had been exposed, he had kept a much lower profile than in the original story.
When he finally appeared before Yan again, it would be when Uchiha Obito had regained enough power to contend with Yan. Without the strength to contend with him, showing up would only make him a little brother.
There were only two ways to grow stronger. First, retrieve his Sharingan—but even if he got it back, the increase in strength would be limited. Second, gain control of the Rinnegan's power.
That was why the final war would begin after the Eight-Tails was sealed.
Because Obito couldn't wait to obtain the Rinnegan, strengthen himself, or rather, take control of the Ten-Tails.
Merely obtaining the Rinnegan would still leave Obito as a little brother before Yan, because he could not wield the Rinnegan's power as he pleased.
Only by becoming the Ten-Tails' jinchūriki would Obito have the capital to turn things around.
Therefore, A could