At Google, when you develop a service, you as a software team are responsible for maintaining it. This includes being oncall. But, depending on how critical the service is, you'll get bonus pay for this oncall time. This can amount to >$10k a year. And your oncall may not be that noisy. That is something and (IMHO) significant. Generally you'll be oncall for a week but this can vary.
For sufficiently high profile services, oncall may end up being owned by an SRE team. That's not really something that can be thrown over the fence by SWE teams. SRE teams have to accept that ownership. To do this, it requires meeting standards like having an oncall runbook, a sufficiently long history (~6 months), adequate metrics and so on. At that point, SWEs will still be second level support for something SREs may need help resolving. You'll still get paid for this.
SREs don't generally have week long oncalls. For the highest profile services, SRE support is global, meaning you'll have team members in 3 time zones such that whoever is oncall is in their normal working hours. So you might have an 8 hour oncall every week or something.
At Facebook, generally as a software team you'll be responsible for that service forever. Some key services may be fully or partially supported by PEs (Production Engineers). PEs are less common than Google SREs.
You don't get oncall pay at Facebook. It's simply expected. Depending on your management, you may be expected to do that oncall and everything else you're supposed to be doing.
So here's why Google's system is better than Facebook's:
1. Oncalls, in my experience, tend to be a lot less noisy at Google. Services tend to be much more mature and stable at Google than Facebook;
2. Teams are generally larger at Google. This means that not everyone needs to be oncall. This is good. There is an optimum size for oncalls. IMHO it is about 8-12. Fewer than 8 and people are oncall too much. More than 12 and you lose skills by not using them often enough.
3. The pay is really important to (2) because it means that those who are oncall at least get compensated for it. At a minimum this sends the message that oncall is important and rewarded. It also means those oncall are less likely to resent those not oncall, which might well be the case if you're not compensated for the extra work;
4. There are a ton of orphan projects at Facebook (IME). By this I mean some product team (in particular) will develop something, ship it and then... forget about it. Onwership of source code trees and projects tends to be fairly strictly enforced at Google. These orphan projects tend to create a number of support issues and tasks that are a drain on oncall as there is no one to pass those tasks on to.
5. Culturally, Google seems to acknowledge and respect oncall work load more than Facebook does. For example, tasks at Facebook have SLAs and I saw plenty of games played to avoid dealing with tasks. Examples: changing priority to increase or remove the SLA, silently closing tasks, passing tasks back months later to the reporter asking "is this still an issue?", etc.
So my point is that not wanting to be oncall is understandable but for many engineers, it's going to be part of your job. If so, you need to make sure your organization does it well. There's a world of difference between an oncall you don't get paid for that's 40 hours of work vs one where you get 2 tasks a week and you're getting paid for possibly having to answer an alert.
Hating oncall is indicative of a bad engineering culture IME. Things like prioritizing shipping above all else, not rewarding fixing things, unreasonable management driven deadlines and so on. Oncall is the canary in the coal mine for all of that.