Hell, they could have skipped the sequence altogether if necessary, starting the prep before a commercial and coming back in with the separation done and a log entry filling in the blanks.
That. If there must be another reason not to do the separation I think it was because 1) it was useless (except for the pilot "look new sfx that we couldnt do in the 60s" scenes) and 2) the battle section alone is ugly.
Ugly because the designer (Probert? Sternbach?) never had the chance to do a proper separable design.
In another example, the ship from that VOY episode separated in 3 parts and all of them looked alright. They even thought to make a tiny pop-up warp nacelle for the section that didn't have them keep able to warp.