I just took a long day hike without my poles, carrying the load I would normally carry for a two-night trip (including food and water.)
The verdict: While I didn’t really need my poles to maintain balance or stability, and didn’t have any problems on uphill or downhill stretches - I unexpectedly found that I missed them! In particular, I missed the way they help me maintain a hiking rhythm; I found myself hiking too fast, or too slow (if there is such a thing), and was having to consciously pay attention to pace.
Most of all, I missed using a pole to prop up my pack so I have something softer than a tree or rock to lean against (or so I can sit with the group, instead of off by myself because of where the tree or rock are.)
I also found one other potential problem: my tent is not free-standing. Occasionally, I’ll camp on a surface that is not amenable to tent stakes (roots, rocks, or an exposed rock slab.) When I do, I can use my poles to hold the ends apart, converting my tent to almost-freestanding (enough for a night, anyhow.)
So, even though I don’t need them at my current pack weight, I’ll probably continue to take them.