Do you really drink heavily when you are on-call?
But I had seen a good attitude from a colleague once: If you want me to put my normal life on hold for on-call shifts, that is fine with me. But then you need to pay me for that time as if I was sitting in the office: "So I'm going to be paid an additional 128hrs the week I'm on call, okay?"
In the specific case it was not about drinking but about weekend or evening trips with the family where the company expected the employee to sit at home instead and wait to potentially be paged.
People quickly came to the conclusion that some lowered expectations for the on-call person would be appropriate and working via a 4G connection from a notebook is totally acceptable.
I would say the experience is transferrable to drinking. Don't drink yourself into a stupor is sage advice, but we're not worrying about a bottle of wine, especially if it's shared over Dinner or such.
I'm not judging, but just pointing out that I've certainly experienced a different OC culture in the US.
And that value is usually defined by the likelihood of incidents and the impact of these.
If you constantly have incidents that are critical, you can either spend the engineering hours to fix the problems once and for all. If that is not possible because it's a different problem every time, it might be important to invest in more engineering resources and have them work shifts.
Printing for example has such a system where the impact of a stopped printing press can be catastrophic because no newspapers tomorrow. Thus there are on-site engineers that are paid to sit around and wait for a press to stop working.
If the occurrence of an incident is rare or the impact of them is basically nil for whatever reason, feel free to consider on-call not that important. Maybe an SLA of 6 hours is acceptable in such a situation.
If incidents are happening often and are important yet you do not want to spring for extra engineers but have your existing staff work on these on top of their regular duties, you need to come up with the right incentives. Massive pay helps to sweeten the deal and also provides incentives to prevent pages.