You're certainly correct.
Generally, I refer to the dumpster fire in the White House as "Team Biden" for exactly the reason you specified.
But in some cases, I refer to the senile creep personally, and by name, simply for the sake of brevity. I feel that's important because my memes are often too wordy. And, if nothing else, the president bears the responsibility for what happens in the executive branch of the government. That's true whether he's only a figurehead or not, lucid or not, even conscious or not.
With this particular meme, I was going for a concise message, unlike how this comment turned out.
Cheers!