NJ, I'm a big believer in trekking poles on the downhills, regardless of how much weight I'm carrying. I'll tuck them away on level ground, and often on uphills, but they always come out for the descents (was it a descent where you fell?). They can be a pain at times, but on uneven ground they add so much more stability to your balance. I've used trekking poles for years on that premise.
Having said that, about two months ago I pretty much put away the trekking poles when doing my twice-weekly workout hike at my local mountain. I figured, hey, I've done this route hundreds of times before - know it like the back of my hand. I don't need poles for this, even if some of the trail is steep, rocky, rooty, and just plain gnarly!
Predictably, about a month ago, I took my first-ever fall on a trail. No poles + sandy granite slabs + downhill at a quick pace = broken big toe, massively bloodied legs, and wounded pride. Thousands of miles hiked over the years in every part of the country, in all types of terrain, and never a fall while always using poles on a descent (many, many close calls, though). Within a month of foregoing poles, bam!
You'll find that on Whitney there are many, many places where you have to take a long, awkward step down. With backpacking weight, it can be even more awkward. After 11 consecutive miles of descent, poles will be your best friend.
