here's a semi-educated guess on my part.
1) using the arms, especially if not raised above the level of the heart very much (e.g., NOT overhead) will only have a small effect on increasing heart rate. the muscles involved are relatively small cp. to the gluts & quads, and therefore require less blood & O2, bear less wt, & use less energy (even though their use in this capacity may be less efficient for ambulatory purposes than the muscles of the lower limbs).
2) redistributes the workload, i.e. removes some of the load fr/the lower body allowing them to work (if you keep the pace the same) a tad less, so they fatigue more slowly. the idea is somewhat similar to doing,...let's say...bicep curls with a relatively light wt.,...perhaps 5, 10 or 15 lbs. how many can you do with one arm? quite a few, i would guess. now, share the load with the second arm. you'll probably grow bored of curling the 5, 10 or 15 lbs before both of your arms tire. of course in this example it's a 50% redistribution. obviously, using trekking poles does NOT cause this level of redistribution of the workload. the muscles of the upper body are simply too small to be able to handle either the loads or the repetition anywhere near as well as the larger muscles of the lower body. however, they can help somewhat.
3) better balance (perhaps this is what you meant by "smoothing out my walking style"???). this results in less forceful contractions & less work being performed by stabilizing muscles of the spine, back, sides, & abdomen. so, to some degree less work needs to be done by them. for example, most people can bench press heavier wts, or perform more reps before fatiguing when using some weight lifting machines, than when using free wts. balance/stabilization of free wts makes them inherently more difficult to lift. [note: lats & perhaps pects will need to be somewhat contracted to help stabilize the arms for balance so that the upper arm does not rise when it bears some load when using trekking poles.]
4) when ascending, your pects & lats get recruited to help your gluts & quads lift your body. the pects & lats are larger muscles & can bear more wt. the tri's (i.e. triceps), at the very least isometrically contract to keep the forearms partially extended and prevent flexing, and will perhaps, depending upon the grade being ascended, finish contracting at the end of step-up to extend the forearm completely/nearly completely. obviously, less work is being done by the lower body in this instance, w/the gluts & quads getting a slight rest by bearing less of the load of stepping up.
i think it's Leki that has the slogan "Four legs good; two legs bad !"
if anyone has any other ideas, or feel i'm mistaken on any point, feel free to share with us.