The Vice President has no power to stop the President from doing things.
If they are complicit, they can be impeached too at the same time. No amount of savvy gives the VP the authority to stop the President from doing things. Presumably, most people fully don't know what is going on until someone is impeached. That applies as well to anyone else as it does the VP.
The people choose the Vice President by voting for the ticket. No one else has this advantage. The Vice President can already have a real coup of the President. They could have the President killed. A coup by impeachment doesn't really make any sense. What could the VP do to get Congress to impeach which wouldn't also implicate him or herself?
If you are going to compare this with someone else, you need an alternative. Do you want a new election? Do you want the Speaker of the House to take the job? If it is the Speaker of the House, then you are going to make impeachments really common. Basically whenever the House and
Senate are controlled by the opposite party as the executive we will get an impeachment so the Speaker can take over.
They would still have to get to 2/3 in the Senate which would probably be rare, but we would end up with the majority of presidents being impeached. The same would be true if it triggered another election. With another election you would have the worse problem of your third point.
There always has to be a President Someone has to be in charge of the military at all times.