If you expect your team to provide 24/7/365 assurance, then it's hard to see how that isn't a perfectly reasonable idea. The only counter to it is that keeping people on call shifts financial cost off the business in the form of psychological cost to its employees. Not very convincing.

Would you take the night shift? Everyone I've seen promote this idea seems to expect that they'll be the lucky ones who get to keep a normal schedule. If you have a service that needs 24/7 uptime, and you transition from an oncall model to a shift model, at least 2 out of every 3 engineers on the team are going to have to change shifts or quit. If the entire industry shifts, high-availability software would simply join the ranks of fields like nursing or manufacturing where many people have no realistic option to work normal hours.