Having managed email queues, the no reply email is essential, because everyone and their uncle uses auto replies. That said, I'm all for including a real email address somewhere so a user can reply.
The auto replies will go to the envelope sender email. I prefer to set that to something like email@mydomain.com rather than noreply@mydomain.com because noreply just looks so unfriendly.
Replies from real people will go to the reply-to email (customers@mydomain.com) and bounces/auto-replies will go to the sender address (email@mydomain.com). You can then write a script that automatically clears the auto-replies and handles the bounces from the email@mydomain.com inbox.
This will allow you to still handle real customer inquiries that come into the reply-to email without being bombarded with bounces and auto-replies.
e.g. in another response someone linked https://github.com/jpmckinney/multi_mail/wiki/Detecting-auto...
Will some things filter through this list? Undoubtedly, but I would be surprised if it's a significant percentage. Extremely high-volume lists probably need some more specific care, to be sure.
If you asked people, one per month would be a 'working' system, if you catch them on a good day. 'Never' is a very long time.