Captain Varley's comments about the state of the Yamato in his logs are to be taken with a grain of salt, he wasn't and engineer. The Iconian virus could do that to any starship, even a Romulan ship was vulnerable to it.
Same thing applies to the Odyssey, it was facing an opponent with shield piercing weapons a ship without shields is always shown to be rather helpless in Star Trek. The captain dropped the shields when they were ineffective against the polaron beams allowing the Jem'Hadar to perform a kamikaze attack, again this could have been any class of starship.
As for coolant leaks and what not I'd say a ship is at the mercy of the writers and the plot of the episode at that point.