We had problems with Chrome for our web editor and do not recommend it for this reason. I am not surprised it does not work for webmail and our song code. Chrome is made by Google who make gmail so it all probably goes through the same systems (coding etc.)
The Mac editor creates a 'normal' computer file if you save it, but it needs to work with our web editor, forum and iOS (and we have a basic version of iReal book on Android.) The format of songs may very well change in the future to make this process more seamless and easier.