They wouldn't wipe out the entire US House and Senate. They would wipe out only those who didn't agree to object to the certification of the Biden's election. They would eliminate Senators and Representatives until Trump was appointed. Now you have an illegitimate president. As you say, the republic is the states, and I don't see how e.g. the Republic of California continues in the Union at that point.
> They are not essential for day to day governance.
Remember that states are not allowed to print their own money as the federal government is. States are now spending vast amounts of money to combat Covid. The federal government is funding these efforts by literally printing dollar bills. If the federal government fails to prop up states, you're looking at states unable to fund hospitals, police, teachers, utilities, etc. If the entire House is eliminated, there's no one to vote on federal budgets, and governors cannot just appoint Representatives as they can Senators -- Representatives must be elected in a special election in their districts according to the constitution. Meaning money from the federal government would just dry up without the House. Obviously the framers never anticipated this edge case.