But any email they send out could be set up to reply right to somebody appropriate. Customers don't want a face of the company that only speaks and doesn't listen. Seems like they should be nearly never needed.
True, if it is a relatively small support operation. This would be harder to do with larger companies that had separate addresses for billing questions, service problems, troubleshooting, etc. If every outbound message had a singular live reply-to email address, then you'd need someone to sift through all those and route to the appropriate department.
Large companies should dedicate the thought and resources to get their customer human interface right. I hate that many large companies that expect customers to navigate through a morass of the companies half-baked organizational scheme. It's a terrible sign if a company expects a customer to coordinate or route an issue among different internal company departments.
If it's a large company, they should be more easily able to find somebody that can sort through the handful[1] of replies to that address a time or two a day.
[1] if there are more than a handful, all the more reason to do something with them - lots of people are replying when they "shouldn't" be!