The primary driver for EMER DESC is to get to where the air becomes breathable. Questionable airframe integrity is mostly a speed consideration, not descent rate. You might elect to not descend at MMO in that case, but the FR24 data seems to suggest otherwise, they kept the speed pretty high.
Unless of course you simply are not in control. But in that case you might think there's enough time to at least place a mayday call, or set the 7700 XPDR (which some people seem to think has been set, but FR24 shows some 55xx code to the end).