If you use Point software you will find both 4506 and 8821. You are correct in stating that the forms must be submitted within 60 days of signing.
This may be BS as the info is second hand but here is what I heard from someone who works inside at CFC. Lenders routinely pull IRS data a certain percentage of loans (checking income) to perform risk analysis. I also heard the percentage of IRS requests ramped up beginning in 2005 because they did not like what they were seeing. So although it appears these IRS forms are not the lender invoked “trump card” that can be submitted years after closing (such as I thought). In the end you do not know what data the lender has gathered immediatley after the loan closed.
BTW: I see nothing in the 8821 form that states the lender is precluded from using the information obtained from legacy tax forms to verify income. It’s late and I am tired but I don’t see it.