Web servers rely on the extensions of files placed on the server to infer their content type i.e. webpage, script, stylesheet, image, video, audio, etc and send that content type information to browsers along with those files so that browsers can consume/render those files appropriately for the site visitor.
Long story short, if Muse publishes pages without extensions, chances are that most of the world would not be able to see those pages correctly in their browsers.
That said, most web servers do offer configurations that allow them to associate *extension-less* URL requests to corresponding files (with extension) on server (e.g. Business Catalyst). However, this requires support and configuration on the server side - which is not controlled by Muse.
Cheers,
Vikas