Frank forcing Walker out was dumb
That just seems like a very stupid way to become president. Walker and his administration were tied to corruption and he was going to be impeached. As his VP, Frank would automatically be tied to that, even as president himself. And as we see in season 3, he has to fight just to be allowed to stay in the race. And even in seasons 4 and 5, he needs to cheat to eventually win his own election.
Wouldn't it have been smarter to just stay as Walker's VP for the rest of his presidency, and then run himself? That was his plan if he got to be Secretary of State. It would take longer, and wouldn't get revenge on Walker, but Frank wouldn't be coming in because of corruption and impeachment. He wouldn't have that target on his back from day 1.