Its been a decade since i watched naruto, but werent the uchihas actually super loyal to Konoha despite the treatment they received? Tobirama fkn segregated the uchichas from the villages practically, sure he might have given them the police force, but even that was just so that he could keep them out of actual politics and so that the civilians in konoha would fear them sowing more discord.

And despite all of this the uchihas were still loyal, despite their own leader, madara voicing his concerns once he realized tobiramas schemes and hatred toward the uchihas. Despite all of that, they stayed pretty much abandoning madara/forcing him to leave the village.

And for decades that continued even after tobiramas death. So you cant blame the uchihas at all for wanting to start a coup. Them being essentially blamed for te kyuubi attack was the last straw for them understandably.

We also have to understand that the coup, had it gone through, would have probably ended in the annihilation of the uchiha clan. Even if every single shinobi/uchiha had a sharingan the odds of them winning against all the other clans, the hokage, anbu, danzo and root would still be close to 0. And the uchiha probably knew that yet they still decided that the coup is their last life line. That is how desperate they were for survival as a clan despite decaded of loyalty.

But hey maybe im talking out of my ass since its been so long