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.
You can configure your email sending with a reply-to email (example customers@mydomain.com) and not have auto replies or bounces go to that reply-to address.
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.
One mistake per day is enough for the knives to come out. On a big mailing list, think about how many 9's of accuracy you have to have to keep one incident from happening per day. Per week. Per month.
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.
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.
The auto-reply is probably sent by a desktop email client, which are often offline and/or configured to only check for new email every few minutes. So you'd fail to mark a lot of auto-replies.
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.