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Senators can only be expelled by a 2/3rds vote (not happening) and there's no mechanism for a recall. The supreme court cannot scrap the confirmation process, as it's part of article 2 of the Constitution. The president does have powers to appoint officers when the Senate is in recess, so in theory, a simple majority of republican Senators could vote to recess and the President could appoint who he liked. That said, the supreme court ruled against Obama doing this back in 2014 when he tried the same for some relatively minor roles, so there's precedent that they'd have to overturn to change their minds this time. Not a dead cert, though certainly possible.
I think you're right that this is at least in part a fishing expedition for what he can do with the Senate.
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Aha, you understand the system! Could he force an amendment of the constitution through congress? By 'force' I mean naming and shaming everyone opposing him, constant demos outside their house, death threats, investigation of their taxes, harrassment of their kids, petitions in their constituencies.
Trump's unconfirmable appointments are a win for him. He'll get a list of enemies in the senate and he'll try to get them booted out via the recall process. If he ends up with a decent list of rejected appointees he can say there's a crisis of a non-functioning White House and get the Supreme Court to scrap the confirmation process. He really does want the powers of a dictator. He's jealous of Putin and Xi.