Your first point aside, Republicans have been trying to privatize the USPS for decades (though it's definitely the case that many Democrats are in favor of this

Your first point aside, Republicans have been trying to privatize the USPS for decades (though it's definitely the case that many Democrats are in favor of this too for whatever reason). The White House has been actively rejecting the idea of providing aid to the USPS over the last month or two despite the fact that the situation has demolished their revenues. I think it's at least quite plausible that the WH could try to do this since it aligns with their priorities, and that McConnell would be fine with it. The House, probably not.