It is not real.
I run two separate profitable SaaS business. Between them, I average about one crisis per year that has me VPN'ing into the box the moment I hear about it. Other, more routine, non-site-has-been-down-a all-night events can wait until after coffee, until tomorrow, or until Monday, depending on what I'm up to at the moment.
It's one of the upsides of running your own show, getting to decide what to make a priority rather than having somebody else on the other end of your pager with a vastly different view of the value of your time
So I agree: It's so much down to priorities, and basically if your pager goes off all the time, you've likely prioritised wrong - it's false economy. Adding an extra server to get the capacity needed to prevent a total meltdown is likely going to be worth far less to you than the time and lost business those meltdowns are. And thankfully when you do things for yourself you get to make those choices.