What are the negatives/disadvantages/hardships with running your own mailserver?
You are
the admin. You rely on the ISP connection and your infrastructure being available. It's doable but can be overkill. When it goes wrong/corrupted mailboxes it's a major pain. You have to be sure that you're not running a relay.
However, there's the alternative which is to use an 'admin' mail client to manage incoming mail with accounts on an external (normal) IMAP/SMTP service. You just run a suitable mail client in a logged in PC/Mac account on an always-on device. Then setup rules and accounts as needed, you can redirect elsewhere or move to other inboxes. You don't use this for everyday email access, it's like a Post Office.