This sounds like a silly charade, and it is. But House Democrats are sufficiently worried their Senate colleagues may buckle under the pressure of having to take so many unpopular no votes that they're trying to build themselves a political way out. If the Senate fails to pass the reconciliation bill, only its original bill will have become law, which means House Democrats will be stuck having to defend its unpopular special deals for states like Nebraska and Florida. The self-executing rule seeks to limit their political exposure because House lawmakers can then say they never actually voted for the Senate bill.
Their goal is the same as the person writing those e-mails from Nigerian bankers: Design a process so that even if everything goes wrong, you won't get caught.