You still need an index of your mail for searches and extra metadata for tags, threading, unread status etc. So you need a protocol for requesting this search and a format what how the client can use the result of that search to access the matching emails.

You need to be able to push email status changes out to connected devices, I don't want an alert for an email on phone if I've already read it on my laptop.

You need decisions around how attachments are stored. Most of the time you'll want to store the attachments separately from the text content of the email so clients don't have to download the attachments to access the text, so you'll need to decide on how this location would be communicated to a client.

Plain files are rather bad for multi-user access, if you have multiple users/devices all accessing the same email they're going to need some protocol for synchronization so you don't get data corruption or lost changes.