As I understand it, according to details mentioned in Star Trek: Where No One Has Gone Before
, Gene originally didn't want any ties to TOS when TNG was being conceived. It was to be a completely new series, which meant no Vulcans, Klingons etc. The other staff at the time eventually talked him out of that preference. I don't recall any specific ban on using the Constitution/Refit model or references, but I do recall Roddenberry didn't like the idea of Kirk and company receiving an entirely new ship with an 1800 series registry for the Phase II/TMP era because he acknowledged the Enterprise as a character in its own right, and felt the ship would be "forgotten" by the audience if the crew got a new one.
As for W359, the dialogue in BOBW does imply that the 40-ship fleet was thrown together as an emergency measure, but Hansen also says it was "just for starters" and the Klingons were sending ships that might not arrive soon enough. Perhaps it's not quite accurate to say these measures amounted to scraping the bottom, but were just hastily organized.