> Why should they cooperate with a party that spent the majority of the past four years trying to impeach a legitimately elected President?

Because effective government of the country depends on that, or them not having the votes to matter.

Also, the impeachment power presupposes that anyone subjected to it will hold office legitimately but be abusing that office; someone who does not legally hold office doesn't need to be impeached, as their pretense of exercising the authority of the office is a legal nullity.