Because the Business Catalyst system is the best choice for in browser editing. The Muse version of it is a scaled down version of the Business Catalyst version. And that is the way it should be in my opinion. Clients can mess things up in a hurry.
Upgrading your Business Catalyst site plan should give you all of the most common features for editing content.
In browser editing currently runs on the BC backend exclusively. BC has a rich featureset that supports e-commerce, webforms with data storage in a contact management system, blogging, customer driven content, etc. These extra features are not integrated into Muse currently, but we leverage the server for the running of our in browser editing system.
When you signup for Muse, you get free BC hosting for 3-5 sites depending on your subscription. You can use these "tokens" not only for your site, but for any of your clients.
In regards to IBE and its current implementation, it supports much of the widgets in Muse for replacement of text and images including navigating through different tabs of content, etc. There are certain scenarios that are not supported, and we evaluate where to focus on improvments based on customer feedback. If you have some specific editing scenarios that restrict your abilities please feel free to send me your concerns at email@example.com
IBE has to run on a server somewhere that we control so we can maintain the application. There are possiblities that in the future we may have the ability to allow editing of websites on hosts other than BC using IBE but we don't have anything further to announce at this time.