The failure mode isn't as a tech company CEO. As you point out, if you're the CEO, you have the luxury of defining yourself unavailable as CEO whenever the hell you please. If the website is down out if business hours and you haven't made it someone else's problem that you're paying for it to stay up, it can just be down. No, the issue is as a father/mother/husband/wife/son/daughter to someone's you love dearly enough to consider them family, biological or otherwise.
It's rather dramatic, but the phone call/conversation I could never forgive myself for missing, is the last words of a loved one before they die, whether due to car crash or some other calamity (9/11). Or missing the opportunity to take the very next flight out to see them before they pass. You are free to treat your family, biological or chosen, as you see fit, I just know there are some phone calls I'd rather be woken up in the middle of the night for than miss. Reaching me via cellphone is more direct than trying to find whatever hotel I'm at since I'm on the road as CEO and talking to customers and vendors in person on the road as CEO, so calling my house phone doesn't help.
I gave up my phone as a lead security engineer at a vc funded company, and continued this when I quit to run my consulting firm full time as single proprietorship. Now we are a team of five running a consulting firm and a PaaS.
I spent most of my career as an infrastructure engineer so high redundancy, self healing you can trust, infrastructure-as-code, and follow-the-sun shifts, are healthier for everyone than expecting people to be available to work 24/7.
OTOH I could see my loved ones an extra 20h a week that I now use my phone. I am not sure they gonna say something vastly more interesting in this hypothetical scenario
It's rather dramatic, but the phone call/conversation I could never forgive myself for missing, is the last words of a loved one before they die, whether due to car crash or some other calamity (9/11). Or missing the opportunity to take the very next flight out to see them before they pass. You are free to treat your family, biological or chosen, as you see fit, I just know there are some phone calls I'd rather be woken up in the middle of the night for than miss. Reaching me via cellphone is more direct than trying to find whatever hotel I'm at since I'm on the road as CEO and talking to customers and vendors in person on the road as CEO, so calling my house phone doesn't help.