I never thought of this, but I can almost see this kind of thing happening. Just anonymously vote the big oaf out of office and then lie to your constituents by saying you don’t know how this could’ve happened – “I voted to keep him.” And then get reelected, which is all most of them really care about anyway.
from Conservative Review:
Removing Trump by Senate secret ballot would be a disaster for our republic
Could the United States Senate use a secret ballot to remove President Donald Trump from office? Possibly, but it would be an absolutely terrible idea.
An article published Tuesday at Politico Magazine floats the idea, noting that Senate procedure allows the upper chamber to set its own rules for trying impeachment and that a bloc of just three Republicans could potentially force the issue.