Moving 2/3 of your existing engineering staff to a different shift would raise enormous large communications issues for a company otherwise designed for an aligned workday.
Hiring, say, minimum 4 people to do nothing but waiting for a page would be incredibly wasteful and probably ineffective as they'd have no idea what to do if something went wrong because they didn't work on the system.
It's a weird thing about the software industry only. I've worked for actual engineering companies (meaning: we build things in factories), where having your factory or expensive integration lab be idle for 2/3 of the day plus weekends is not justifiable. People were scheduled in shifts, and they worked those shifts. And although there was a concentration of people working regular day shift hours, there was always a full team on-site (not on-call!) 24/7. If you weren't on-site, you were never expected to be on-call.
Is that really weird? In a factory, time is produced things is money. 3x shifts is 3x things is probably close to 3x, at worst 2x money. In software development we've long learned that with 3x as many developers you're lucky if you can keep the same pace on the project, let alone improve. (It could be 2-3x as many projects, but then you have 2-3x as many operational problems again.)
And then you have companies like HP that outsourced to India, East Asia, and Eastern Europe and then found that they could have 24-hour employment shifts through timezones. Shared integration and testing infrastructure got reused between teams working on different aspects of the same problem. Support requests got handled by whatever team was online when the request came in, and written up and handed off to the next if the clock struck 5pm.
Hiring, say, minimum 4 people to do nothing but waiting for a page would be incredibly wasteful and probably ineffective as they'd have no idea what to do if something went wrong because they didn't work on the system.