hire more people?
Hiring more people is a great idea for making on-call less stressful, because it allows for much sparser on-call shifts (e.g., one week every 8 months vs. one week every 2 months). But I don't see how hiring more people gets rid of on-call completely. Someone will always have to be on-call.
You cannot just hire people who do on-call-only duties and nothing else, you have to be very closely familiar with the code and features being written in order to resolve issues effectively. Which usually means that you need to be someone who actually worked on those things, not just some glorified extra-fancy customer-support worker.
Being effectively at work 24 hours a day for seven days straight sure sounds like a recipe for burnout to me. As TFA notes, these people aren't doctors, the only thing that happens if a glitch takes two hours to fix rather than one is that Amazon loses some money. Amazon naturally would prefer not to lose that money, but its workers presumably would prefer to be able to sleep too.
If a big selling point of your system is the ability to be on 24/7, on-call is inevitable. But it definitely can be way less gruesome than it currently is at Amazon for a lot of teams right now. For example, my on-call schedule is extremely relaxed and low-stress, it is never a worry I actually have or something I dread ahead of time. But getting rid of it completely is simply impossible for a lot of "always online" services.