Again, this will depend HUGELY on what sort of role it is (an external-facing vendor, for example, should probably not use something like this). But for many internal requests, it is not power-tripping to ask someone to either redirect their email or wait until a later date to send it.
As an employer one of our policies is to Call in absent days not text them in. This hasn’t worked well as employees ( especially young employees) will still text in those types of messages. It would be wonderful to have a feature in the iPhone that allows for instant text response that can be set up for certain contacts( employees). Something similar to an out of office message in email…” I am not receiving text, please call … … …. and speak to me directly”

My project is entirely phone based and we don’t have voicemail, either for the project line or individual staff lines. We used to, but we found we spent so much time returning voicemails and getting people’s voicemails that it led to us missing calls and going in an infinite loop.
It got bad enough that others began begging someone to cull the list. Reply all, of course (thankfully it didn’t turn into an explosion of replies all). Someone finally did remove the email from the list.