Iirc the first and only attempt to impeach a supreme court judge involved one with an obvious alcohol problem.
They know they can’t/won’t be impeached, so that leg of the “checks and balances” was kicked out from the get-go.
She wouldn’t be the first SCJ to be impeached. Samuel Chase was impeached by way of the Jefferson administration because of his “harsh” sentences for corrupt Democratic-Republicans under Adams and Jefferson. He was acquitted because it was determined that he couldn’t be impeached for his political beliefs.