I often wondered why Riker didn't separate the ship in "Final Mission". He acted as if the ship couldn't be in two places at once.
I doubt the saucer would have done any good at the crash site system, really. For all we know, the battle section would have reached that system faster than the saucer even if delayed by several days...
And the barge-towing features much more puzzling elements than the failure to separate the saucer. Why tow the barge in the first place? The only location where it did any harm to anybody was on low planetary orbit, and Riker got it out of there early on in the game. Letting it float right there, or crash into the asteroids, would have seemed far preferable to towing it all the way into the sun. Why the sun? The barge won't stop being radioactive merely because it gets vaporized. If the radioactive vapors are harmless at the distance of the sun, why not let the barge coast to an equal distance in some other direction, free of asteroids? It would even take less energy; it's notoriously difficult to slow down orbiting objects enough to get them to fall into a star, in comparison with just giving them a kick away from said star.
Riker appeared to be looking for a quick fix, perhaps because of the Picard diversion. The local sun is a good garbage dump site in one sense, and one sense only: it serves as its own quarantine marker! And the towing did take place very swiftly and before any real radiation damage was suffered; stopping to separate the saucer might have caused a delay for no real benefit.
Of course, the mystery of the countdown on radiation damage remains unresolved as well. Why would any particular timepoint be so significant? Why would damage suffered before that timepoint be irrelevant? Or conversely, why would damage suffered after the timepoint be irreversible?
Crusher speaks of a balance point after which hyronalyn won't reverse the effects, apparently meaning not at the rate they are being inflicted. If the ship went beyond that balance point, perhaps effects would finally start accumulating in the patients - but couldn't they be reversed afterwards with further hyronalyn, once the radiation exposure had ended?
The computer gives a countdown to "lethal exposure", but it may be talking out of its cybernetic ass, and our heroes understand/ignore its weird shorthand because they know Crusher is responsible for determining the balance point and the computer just does what Crusher has asked of it.