No, it requires that you be able to stop whatever it is you're doing and be working on a problem within some latency tolerance (5m and 20m are cited upthread, for example). For most modern datacenter workloads, that can be as simple as "carry your laptop and stay within reliable coverage". While sure, that rules out a lot of activites, most of our lives are spent in that regime already.
And be sober, and somewhere quiet enough you'll reliably hear/feel the notification, and be somewhere you can get that laptop out and type away at it for a while.
I get _much_ less enjoyment from many social activities when I'm on call. I enjoy gigs way less. I enjoy parties way less. I pretty much wont go to movies. I hate being "on call" while out at dinner with friends. I will not go on a date while on call (at least not with somebody I don't know well enough for them to understand the on call obligations).
> most of our lives are spent in that regime already
But not all hours in my life are of equal "value" to me. A lot of the "most valuable and enjoyable times" get disproportionally affected by being on call. I care way less about potentially being paged at 2:30am on a Tuesday morning than I do about having to curtail social events on a Friday evening or a weekend. You _will_ need to pay me handsomely to do that, and guarantee it only rarely becomes my responsibility. Been there, done that, am perfectly happy to turn down job offers that don't understand that (or to walk away from companies who try and spring that on me later I've accepted).
Technically this is not a requirement. I've definitely known people going oncall while tipsy or at the pub, as long as you're not shitfaced drunk and physically unable to answer the page. Not that it's something I'd ever do or recommend doing, but it's technically not forbidden.
There are plenty of things I do in my own time that can be interrupted: books, movies, HN, housework, etcetera.
Software developers aren't special, were not even operations staff. Just build stuff that fails gracefully and deal with it on Monday.