In my experience, customer facing professionals are often quite bad at gauging the actual importance of client concerns, and good at magnifying them. I certainly was.
Scheduling adequate coverage is ultimately a concern for upper management. If they allowed "critical issues" to go unresolved on anything other than a rare occasion, the issues were probably not critical to begin with.
It's not necessarily only about the importance of the actual concern or question.
In my experience, customers appreciate it a lot if you get back to them in a timely manner (~30 minutes), regardless of how trivial the issue or question is. It helps you build a reputation as a reliable businessperson, and further helps you build a good relationship with that customer.
Of course customers like being acknowledged, but that's the responsibility of whoever is actually interfacing with said customer. IME, it's pretty unusual to need developer input just to adequately respond to a client. It's also quite unproductive to run around context-switching developers every time a minor issue arises.
This is why I specifically mentioned that this is an upper management concern. Those in client facing roles often default to wishing to provide the best possible support to their customers at all times. It's a good instinct, but that doesn't mean it's always the pragmatic course of action.
We try hard not to context-switch developers. For most issues, email is used, and that allows them to respond whenever they want - as long as it is within the same day.
But if the issue has been outstanding for a day, then we resort to instant message. Context-switching does occur there, but that's the price one pays for leaving at 2pm the previous day when a lot of customers were still at the office working.
Scheduling adequate coverage is ultimately a concern for upper management. If they allowed "critical issues" to go unresolved on anything other than a rare occasion, the issues were probably not critical to begin with.