Maybe not in 1860s culture?

I don't know, this is just speculation. Mainly because the cost of producing a duplicate letter (for ones actually sent, not this case) was sufficiently high that I assume there wasn't a culture that could make use of such duplicates.

C is for Clean

I don't think this is a reasonable interpretation of an unsent later. The point of creating documents for the purposes of CYA requires them to be publicly recorded otherwise there will be accusations that the document was created after the fact.

There's really no reason to believe this was a motivation for Lincoln to write a letter, particularly because there is no clear reason for him to be concerned for CYA. The only people Lincoln would be accountable would be the voters, and I don't see producing a letter blaming Meade for letting Lee escape to be something that would pass muster. I mean, what's the argument here? "I was angry at Meade at the time, and here's the letter proving that I was angry"?

So it seems reasonable to conclude that this is an example of anger management, and not a political back up plan.