In addition to points and observations that have already been made about the benefits of trekking poles, I'll add that I find poles most helpful on the mixed terrain trails that I encounter and a little less important on well-groomed AT-type trails. On these types of trails, having four points of contact with the ground, instead of two, allows me to keep a more consistent pace. When you go from a groomed trail to stream, wet slab, mud, groomed, rocky trail, snow, rock slab, icy slab, etc. punctuated with blow-downs and piles of rocks.
Also, although I have several dependable hiking/backpacking partners, the last few years I've found that 2/3rds of my trips are solo. Sometimes while solo hiking without poles, I've found myself "spacing out." With poles, taking care with placement from time-to-time has helped to keep my mind a bit more active.
Overall, I don't find poles to be a burden. If one day I do find them to be a burden, I'll leave them at home. So, I'm not really too worried about it.