My employer is not a startup (financial bank) but we use a technical "noreply" account for sending automated mail to our users (no external services, they're sent through our mailserver). We use a noreply because the same account is used for different kind of notifications (to clients, to financial advisors, to internal users, to external parties etc..) and we have different inbound mail accounts for assisting them (and actually the main channels for communicating with are web trouble ticketing and toll free number, mail is not the suggested one).
Having said that, I must admit that the whole system is quite basic and not integrated as you'd expect for serious problem tracking (ideally we should use something that can keep track a problem through different channels, integrating web, mail and phone ticketing).
N.B. one problem is that unfortunately there are tons of people who cant read and dont understand that if you write from a "noreply@domain" account and write in the mail "THIS IS A SERVICE ACCOUNT PLEASE DO NOT REPLY TO THIS MAIL", you're actually supposed not to do it
This might be your point (didn't quite get your point) but that's exactly why you should fix this. You actually have separate inbound and outbound channels. It's rediciously simple to change those outbound channels' email addresses so that a direct reply will be sent to the corresponding inbound channel.
It doesn't matter if the system is basic and uses a smtp server or if it uses a hot new email routing service. It's about setting the correct from address in your systems code.
The automated outbound mails are mail like "you have a new trouble ticket, please login to your personal area" (maybe because they forgot to send us some documents)
They dont have to reply to the mail, they have to login and reply via the troubleticketing system, eventually uploading attachments.
if you set the from address as you suggest, but you dont have a fully integrated (mail/web etc..) ticketing system, you end up with a mess (part on the web part on the mail account).
Once you figure out the right question, you can probably figure the answer out on your own.