This does not jive with my experience. Most companies aren't Google as you've described it, and in most cases the person on pager duty is the first human examining the incident.
> If there was a sleepless night
How about if they get woken up each night for an alarm that turns out to not be a big deal? That is the typical on-call experience, getting woken up for 15-30 minutes each night, cortisol from 0 to 100 in the 15 seconds it takes to get into Work Mode.
I guess that doesn't qualify as "sleepless" but between it and the general stress of not being able to turn the phone on silent, I'd call it "shit sleep." Nobody should be subject to it. How can you expect somebody to produce decent software in this condition?