I take that a step further, "absolute emergency" is rarely an "emergency".
Based on my experience, it mostly translates to whatever task the person thinks it's important for them. Sometimes people will mark the task as "urgent" just to dump it on someone else.
The other thing is, in critical emergencies, you should work slower than usual. This means muting all notifications and taking your time. Rushing to get things done can exacerbate the issue.
Best engineering managers shield the team in those situation and simply reply with: "thanks, we've been notified and investigating".
What is the problem with replying instantly? If you can give a reply immediately why wouldn’t you? If it’s low priority work that takes time, sure, but a typical yes/no, I’m available at 5, whatever, why not just send it?
If you’ve already read the email it’s less efficient to come back to it later
Also, email delivery in general can be delayed for hours. It’s not common, but there are no delivery guarantees around email. You could reply immediately, and it could arrive in their inbox much later.
I once built an IdP that vended access one time codes via email. We had to switch to other means because there were a small (but significantly high) fraction of customers who didn’t receive their OTPs before they expired (TTL was 15 minutes). Also even if they came in before the TTL, a user experience that involved waiting that long to get logged in was not tenable.
you can shorten this to "never reply instantly", because an "absolute emergency" will never be communicated by email.