why would Bill agree to be traded?
I get why NE would prefer that. They get to control where he goes, do the whole "we don't want you but we also don't want you to succeed somewhere that might hurt us" dance.
If any coach has earned the right to either stay or decide his next landing spot it's Belichick.
That said, maybe he wants to go to Washington for some reason and the Patriots are happy to help make that happen, so they sign him to a massive contract to ensure he is taken care of if it doesn't go well there. I assume the contract comes with him if there is a trade.