This answer is from personal experience and personal observation in Yosemite and the other parks of the Sierra. (I wish I had time to research this answer properly, but I don't right now.)
The altitude above which fires are prohibited is what I call continuous timber line, which is probably not an official or scientific term. It is the altitude at which woods give way to scattered small islands of trees in a sea of granite. This transition is quite abrupt. May Lake in Yosemite, for example, is surrounded by woods, but a few hundred feet above May Lake there are only small scattered islands of smallish trees.
There are expanses of granite with few trees well below 9,600 feet in places in the Sierra, but these are islands of granite in a sea of trees.
Only yahoos would cut branches off living trees or (shudder) cut living trees down. Park regulations call for collecting only downed wood, of which there is plenty below timber line. Two good follow-up questions might be whether timberline is moving up as the climate warms and whether the Park Service is investigating prohibiting campfires other than in official campgrounds because of the increasing danger of forest fires.