Given the disease aboard the Exeter, destroying it would have been the prudent thing to do.
Immunizing the crew would also be possible, although logistically demanding until somebody figured out how to replicate the health-protecting qualities of the Omega IV environment in laboratory conditions. Imagine the possibilities: a starship the enemy can never board and conquer, because they turn to dust in minutes! Indeed, Starfleet might do well to contaminate all its ships this way, and then install immunizing facilities at the shuttlebay and the transporter rooms, so that only authorized guests will survive...
The Excalibur could have been repair where it was to the point it could have gotten to a repair facility under it's own power. Otherwise it would have had to have been towed. Depends on what was actually wrong with it.
The original episode shows no visible damage; the TOS-R version shows some charring on the saucer. Yet supposedly, such charring resulted in both of Kirk's Enterprises
being immediately condemned to scrapping, in ST3 and ST6, respectively...