alt Hacker NewsFrom memory, there are no bulk actions, so if you want to say select all emails and delete you have to send thousands of requests. If you want to rename a folder you have to send a request for every email in the folder. There is no way to set up filters that run server side, there is no way to get push notifications.
And probably a million other things that don’t hold up today.
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Sending those thousands of requests is something your mail client does for you. Deleting 5000 emails takes a few minutes, but how often do you do that? I can select a bunch of emails in Thunderbird and just do stuff with it just fine.
For server side filters I just set them up in Fastmail using the web UI. That's the type of action I do once or twice a year, so totally OK to hop on over to the web app for just that.
I have no idea what you mean by 'push notifications'. I have Thunderbird open on my desktop, and it shows me when there is email. I have K9 on my smartphone, and it shows me when there is email (I don't have it set up to display notifications, but that seems possible). That's basically all I need to do email.
Deletion is done by marking messages with deleted flag and then expunge to delete flagged messages. AIU rename exists: https://datatracker.ietf.org/doc/html/rfc3501#section-6.3.5
Push notifications: https://github.com/freswa/dovecot-xaps-plugin