Time difference between admission offers and rejections in US PhD Admissions?
Both your reasons are in play, although the second far more so, in the math dept at my "R1" university in the U.S. That is, we make a certain number of offers to well-qualified people, expecting a certain approximate rate (perhaps 50 percent or more) of acceptance of our offers, with considerable variation. We cannot risk far too many acceptances, because of funding limits, but, at the same time, we need a fairly precise number of TAs for the following year. So after we receive some rejections from that clear-first-round bunch of offers, we can (and must) make the corresponding number of second-round offers. Inevitably the number of such is not zero, but is unpredictable, and the financial set-up is such that we do not want to risk over-committing... and under-committing for too long risks students already being informally (if not formally, since nothing is set until until April 15) committed elsewhere.