Whether or not the shōgun was a figurehead depends more on your definition of "figurehead" rather than reality.

I talked before about the power balance between the emperor, kanpaku, and daimyō. A similar situation existed for the shōgun: he had a lot of legal authority, but his personal authority was often quite weak due to being deprived of income from his own lands and unable to mobilize significant forces that answered directly to him. Many powerful daimyōs took advantage of this to oust disagreeable shōguns and installed ones that would listen.

However it is important to recognize two things:

1. The shōgun's orders were still quite often followed when possible, especially by provincials daimyōs and samurais not directly fighting against him, even if the orders were not very favourable to said provincials. Appointments and approvals by the shōgun were also very much still favoured and sought after by said provincials as well. I gave a couple of examples in the linked thread.
2. The shōgun very much knew their own situation and tried to change it, there-by becoming important, powerful players in the political game. Ousted shōguns looked for supporters to help them retake the position and many answered these calls. Shōgun who reigned in Kyōto often ended up disagreeing with the daimyōs who propped them up but left them out of the decision-making process, which would often end with said shōgun and daimyō coming to blow with each other and supporters having to pick sides and, yes, to the shōgun's ouster or even death.

So shōguns were not just rubberstamps who existed purely to say okay to whoever that happened to have the largest army in Kyōto, like how we might categorize modern constitutional monarchs or other head of states who were not also head of governments. Shōguns were men who had their own personalities, their own goals, and used the position's authority to further their wishes, even if those wishes went against the daimyōs that supposedly was in charge.