To answer your first point. The functionality to export data from Audience is not available yet. There are export buttons available on other views of ACS but this specific thread is for Audience only. If you wish to have this feature provided please reach out to support and share a feature request with them.
Now, the export functionality provided by ACS on various screens does have an upper limit. If the volumes are high you won't be able to export the entire data. This limit has been imposed to ensure someone doesn't consume entire disk space and memory to export huge amounts on data.
To answer your second query, if the file gets exported on app server, end users cannot access them. As a result of this, we have File Transfer activity on workflows to transfer these files to Adobe sFTP provide with each instance of Campaign Standard.
If you don't have one, please check your contract and request Adobe support to get the sFTP created accordingly.
Ok, thanks, I have a couple questions in response:
This may sound a bit sarcastic but it is an honest question and not intended to be rude - by "not allowed" do you mean to say that the functionality doesn't exist yet, or is there a specific reason why an Admin with full privileges is restricted from exporting to their local machine?
How do I access a file that has been exported to the App server?