I don't think Stannis will fully defeat Ramsay or capture Winterfell in the books. Most likely his campaign against the Boltons will be lengthy and messy, but he will eventually go down around halfway or two thirds through the Winds of Winter, at which point resurrected Jon will show up and finish the fight that Stannis laid the groundwork for.
If that were true it would be understandable for them to let Stannis die more quickly and spend the full budget on Jon Snow's battle . It was unfortunate for Stannis though, as his downfall was so rushed.
I'm not sure exactly how reliable the source is, but I remember someone supposedly read an early draft of the script for Season 4 Episode 2 (written by GRRM), and among other things there was a note that "Ramsay's hounds will go up against the Stark direwolves in a season or two, so we should build them up now." If it's true, then that was probably something that got cut due to budget from the Battle of the Bastards, but it shows that it was long expected that Ramsay would come into conflict with a Stark.