I am looking at my last two boxes of resupplies I am about to drop at Parcher's and Reds Meadow, wondering if I could do without the stove. Maybe for a while, but not for a long hike. Just the lack of coffee in the morning would drive me out of the mountains after a week. It all can be done, but it's just not worth it to me.
Long ago, I hiked without any stove or intent to eat anything warm, and then I shared a camp site with another hiker who had pretty much the same ideas about mountains and how to travel light and affordable, however, he had a stove. He cooked me some wicked spaghetti, with a little French wine we picked up that day, some fresh onion, tomato paste, cut up salami, yummmie. I don't think I ever went out into the mountains without a stove again.
For a summer Whitney climb, though, I don't think you need any of that. We are facing a 3+ week trip starting once our car gets fixed here in Bishop, hopefully tomorrow. Just to keep the morale of my son at above 50%, we need some really good warm meals in the evenings, warm drinks for breakfast. That's all we need the stove for, but it's so worth it.
