FARs call for holding cabin altitude below 40K feet at all times and not allowing it to go above 25K feet for more than 2 minutes. The "never exceed 40K" bit is not too hard for subsonic transports as that is about their cruise ceiling. The depressurized emergency decent challenge has always been the "not above 25K for more than two minutes" bit. Some of the more recent slippery designs have a real challenge generating enough drag to get down quickly enough to meet this. Starting at a higher altitude would bring the "never above 40K" into play and make the time to get below 25K even more of a challenge.
An interesting twist is considering use of a scoop to channel air into the passenger cabin in the event of a depressurization. If the scoop has a large enough cross section it should be able to pull enough air into the cabin to counter any hole up to the size that must be considered for certification. An interesting / troubling consequence, however, is that the process of compressing outside air via such a scoop could end up heating the air to an unacceptable temperature. You are left with two unpleasant choices, have cabin pressure drop well below that for 40K feet, or cook the cabin in the process of repressurizing via a large scoop.