The alternative viewpoint is that rolling the in-the-money call consists of 1) closing the call at a loss, and 2) selling a new call. On considering this further, I think those two actions should be independent.

The loss on the expiring call is irreversible. So why should the strike and expiration of the new call depend on how far underwater it is?


I agree in principle. And stated so long ago on the former TMF boards (R.I.P.)
This is exactly how my broker reports the transactions. I think that the main purpose of thinking of it as one long running transaction with a little hiccup in the middle is to fool oneself. Plus the erroneous mindset of "It is not a loss until you sell".
A.K.A. "sunk cost fallacy"

Oh well.

Etrade, and probably other brokers, has a "roll" transaction type, where you put in the existing option and the new option (new strike & expiration) along with the net credit or debit. This leads one to think of it as one transaction. But when it fills, they show a sell and a buy transaction, not one.

So logically, you should select the new option you are rolling to the same way you pick any new option -- and pay no attention to the strike and duration of the old option you are rolling from.