Sorry but this all sounds lazy to me. If there are any real customers using the software they are going be rather unforgiving of your desired work ethic. Perhaps in a large org with a staggering of staff this could work... But would be challenging to keep the continuity throughout the work week. Certainly an interesting idea for the larger orgs.
The above, and I'm on call 24x7x365 although I only get a call about once a month.
Also both the company and I have a motto of fail gracefully. So the automated testing system and the ticketing system decide they're not on speaking terms anymore, well, we could all set our hair on fire and run around and scream, or just buckle down and do it manually, 5x as slow and much more error prone than my integration system.
They expect me to fix anything 24x7 or have an excellent excuse (most recent excuse was my kid is in surgery so I'll go home and log in later) but they only expect me to invent or create new stuff in a much more restricted set of working hours (And the end users have absolutely no idea what those hours are...). Actually they're pretty pissed off at me if I make any production changes outside of certain work hours, unless I have an excellent excuse, so in the ebb and flow of work sometimes I have to read HN until I get the mgmt thumbs up if there's nothing else on my plate.
Enlightened self interest provides a strong motivation to automate the hell out of all error recovery and have backups to the backups. My systems for error recovery and resumption of production are much more complicated than the actual production itself, most of which is fairly simple although on a very large scale. I literally can't remember the last time I was woken up at 2am, although it could very well happen tonight...
(Oh and edited to add, I don't work in Ops. A drive fails in the NAS, a vmware server needs rebooting, they take care of it, that type of thing. The problems I get involved in after hours are higher level than ops, like somebody thought it would be funny to upgrade the software on a testing machine removing my access, or they changed firewall rules without telling anyone, that kind of thing, big fun)
