I’m not sure if the explanation in the second part holds water. Wouldn’t the reduction in property value be the same as the ammortized free rent?
Don't forget this is typically a short term things. When the economy improves the building will be rented again. So they need the books to look good today to get through.
Commercial loans are often shorter duration and roll over and highly tied to the valuation of the property or properties, and often have clauses allowing them to call the loan if valuation dips too much (think: margin call).
In my experience in many cases this is not true. The shift toward online shopping, for instance, has meant that a lot of retail properties have no realistic chance of recovering to previous values. The accounting shenanigans described in this thread are just a way for various people to play make-believe that their properties haven't already lost value permanently.
If the lender insists the property be valued based on actual collections rather than hypothetical collections based on the rate once discounts expire or the asking rate if vacant, then they will have a loan where the borrower is underwater and that's going to end up as a loss on the bank's books.
If the borrower values it factually, they will be underwater and likely have to sell for a loss or be forclosed on.
There's also portfolio effects. If rent drops are acknowledged in one space, nearby spaces may also acknowledge lowered rents and most banks have lots of loans and many borrowers manage several buildings.