Yep, the export to disk only appears if the asset of the theme you're editing has a presence in the /themes directory. Otherwise, there's nowhere for it to save/sync to.
And yes, if your theme files are on the server, you'll need ftp/rsync to get at them after saving.
As far as "make a copy of this textarea" is concerned, I'm not sure. What's the use case, just out of curiosity? What do you intend to do with the file after you've saved it? Is this for version control of individual files?
Also, would the export take the current copy of what's in the textarea - that may not yet have been saved - or take the last saved content from the server (as far as the database/file system is concerned)?
given that we can write theme assets to a writable location, are we missing a trick by not offering to save config.php in place during install?
Yes and no. Yes, it could be done (test if writable and give it a whirl, then fallback on download if it fails).
No we don't do it because that file is so massively important, it's a security risk to permit it to be overwritten from a browser. If someone doesn't delete their /setup directory, anyone could just blat the config.php. At least the way we have it, there's an air gap - albeit not the most user friendly method to adopt.