The Constellation class were never a back-up plan for the Excelsior. The USS Constellation itself went on a one year trail run even before the Excelsior had left the shipyard.
But in real life. The four nacelle prototype Excelsior, did lead to the idea of the Constellation.
As for the other replies, I'm sure there was plenty of internal Starfleet politicking to get the Constellation class approved and to protect it once the Excelsior with conventional engines turned out to be viable. I can also see the argument for the Miranda's popularity and the Constellation coming from their shuttle bay volume.