Search is built into the IMAP protocol. [1]
Filtering doesn't belong at the IMAP protocol layer anymore than it belongs at the SMTP layer. That said, "Sieve" is really powerful, and there are many SMTP and IMAP servers which support it.
> Filtering doesn't belong at the IMAP protocol layer anymore than it belongs at the SMTP layer.
Right, so users are forced to set up this stuff for each and every device they have. This is a big reason why the exodus to webmail and the proprietary internal-only protocols they use.
Seive is really powerful and I've used it plenty of times, but it's not standard and is something that needs to be done completely separate from almost all email clients. Unless you are a big email nerd that runs your own servers it's pretty much worthless.
You can get desktop and web based and command line clients which talk the ManageSieve protocol so provide you with an interface to manage your server based sieve mail filters [1]
I'll agree that it's not common. Not because there is anything wrong with it, but because companies like Google decided to roll their own for whatever reason.
I can see use cases for needing to search across multiple folders. I guess I've not felt the need to do that myself before. However, no reason your IMAP client couldn't search folders one after the other, or open multiple connections and search multiple folders simultaneously.
It is, actually. https://wiki.tools.ietf.org/html/rfc5804
> something that needs to be done completely separate from almost all email clients.
In that it is not part of IMAP, yes. However, webmail clients like Roundcube and desktop clients like Thunderbird and Claws/Sylpheed all offer plugins.