YES! And Mail.app on OS X actually works better with FastMail's Archive than it ever did with Gmail's (in my experience).

Here's a screenshot from Mail.app: https://files.app.net/1/79773/aTOWGMJ-rQ2Js_Edg-CWLi5FsLEVYq...

I either never knew that existed when I tried Mail.app with Gmail or it didn't work. In any case, it works perfectly with FastMail's "Archive" folder.

No, and it's really annoying. I have an "Archive" mailbox in my Fastmail account, and Mail on both OS X and iOS recognize it as special (they give it the same "archive" icon as a GMail account), but don't override the 'delete' function. I haven't found a Radar for it, but I imagine that many of same have been closed as "works as designed".

Surely "Delete" is more "Move to Trash"?

In our web interface, there are two buttons - one moves to Trash, the other to the Archive folder.

I don't use webmail; I was referring to the way that iOS recoginizes GMail's "All Mail" and overrides the delete function.

Mail.app's "Archive" isn't the same as Gmail's. In Gmail, it just removes it from the current mailbox but leaves it in All Mail. Mail.app actually moves it to a specially-named IMAP folder.

Yes, there is an archive button. There is a difference, mail in Fastmail is in traditional IMAP folders and don't use tags as folders, I assume that you just tell the mail client not to download the archive folder.

Yes, it has Archive.