It was probably was the case in history, but i'm sure Lincoln and Davis should not personally direct each regiment merge... while directing also each military, economic and political facet of the war.
I have enough tedious work at the office. Really, i don't need no more boring and mechanic stuff while playing.

Give me interesting strategic decisions!

The problem with what you propose is that it would not be an option to the players as you say. If we eliminate/heavily limit replacements, we will force every guy to micromanage to death if they want to have anything but an skeleton force on the front. And that is not optional. This is a wargame, so you must have armies on the front to fight with.
Just my 2 cents (form the back row of the SUV too

Cheers!