We can't just chunk these complex systems over the wall and say "have fun with that" and demand more money when the solution breaks. This means we failed to properly estimate total cost of ownership when we sold them the system and now they're held hostage. This is borderline legal breach of contract.
If we told them the true sustainable cost of ownership for a follow the sun support model they likely would have never purchased the solution in the first place and we'd be out of a job.
We could have lots of annoying jobs or no jobs at all. I'll happily accept the former.
I'm not begging anyone to let me prove my technology, I'm working with management to come up with a solution that will work for the customer. Oftentimes management will forbid or otherwise prevent me from using a better, more robust technology that would have prevented more production issues because of short-sightedness. If I pointed this out and was still told to go ahead with the short-sighted solution, and it breaks in production, whose fault is that?
I'm not suggesting the 'it's your problem now, have fun' approach, I'm suggesting the 'pay overtime for overtime work' approach. This is nowhere even near to 'breach of contract', please don't throw around lawyer-like terms when you clearly don't understand what's being discussed.
It's fine to drink of the chalice of the corporate kool aid with moderation. Still, one should never get black out drunk out of it.
It's also the kind of theft that insidiously convinces you that it's really cool and that you're actually OK with it because you're learning how to 'keep cool during crisis'. You know how else your employers could have taught you that? By providing actual training during working hours, while you were being paid.