You are right in stating that it's mostly a matter of energy, but...there is more to it.
Pluto's huge distance makes it impractical (and rather expensive) to change the orbital inclination. The Ulysses spacecraft had a huge inclination to the ecliptic, which required a complicated maneuver near Jupiter to attain. Such a maneuver introduces additional risk, is more expensive, and most of all, unnecessary for this mission's goals:
- Pluto will be near the ecliptic at the time of arrival, which was part of the reason to launch at the time it was launched
- New Horizon's very high speed, necessary to make it to Pluto in a reasonable amount of time, make it completely impossible to enter orbit around Pluto anyway (for which an inclination change is mandatory).
It is also undesirable for its secondary mission goals:
- After the Pluto encounter, it is the intension to push on to the Kuiper belt (which some would even call the main mission)
The Kuiper belt is mostly uncharted, although there are a few known candidate objects being considered for New Horizons to visit. The belt is however expected from an orbital evolution point of view to lie mostly near the ecliptic. New Horizons will therefore have the largest probability to discover new objects, and information about the Kuiper belt in general, if it flies close to the ecliptic.
So, in conclusion: the only technically feasible and affordable option to do in situ measurements of Pluto was to do it in a single fly by, and with less than 8 weeks contact time, of which only a few minutes will in the end be relevant for all the Nature publications that will follow from the mission. The probe will then fly on to visit some Kuiper belt object(s), which are all known to be constrained to a relatively narrow band around the ecliptic. If a significant inclination change had been given to visit Pluto at a different time or under different conditions, this would not have been possible, decreasing the overall expected scientific output and therefore pretty directly also the likelihood of it getting funded.