Sure, so they can seize power for 21 days. And what happens then? They’ve got an enraged president, who will immediately fire the cabinet members who conspired against him, and exile the vice president from the White House. What will you have achieved?
No, to remove the president via the 25th amendment you need two thirds of each house. And if you have that, why bother using this cumbersome procedure, when you can impeach and remove him within a week, tops; and you can do that <i>without</i> the VP or any cabinet members, and with only a simple majority of the House rather than 2/3.