This makes the rounds of the blogs every couple weeks, and yeah... If you use noreply@, you're going to negatively impact user engagement. But in reality, sometimes you just don't have time to talk to users. At least, not all of them.
I have time to provide good service to a limited number of my customers every day. Meaningless feel-good interactions reduce the number of meaningful interactions I can have. I check the no-reply inbox every couple days anyways, and in general the people who send email to that address instead of seeking out the support email on my homepage are the customers I'd rather lose. It's a good filter.
I once spent some time chatting with a guy who ran a handful of fire-and-forget IT side-businesses, including wifi/hotspot internet access.
His customer service philosophy was very simple: either you use and like the service, or he refunds the money. It wasn't altruism, it was self-interest. He didn't have time to do customer support, and was very blunt about it. Either customers corrected their own issues, or they were no longer customers. This was one of the ways he was able to have time for his several companies.
I have time to provide good service to a limited number of my customers every day. Meaningless feel-good interactions reduce the number of meaningful interactions I can have. I check the no-reply inbox every couple days anyways, and in general the people who send email to that address instead of seeking out the support email on my homepage are the customers I'd rather lose. It's a good filter.