Aha, I can answer this one.
> email
One view of email is really reading and composing lightly formatted text with a "send" option. From this perspective, a text editor implementing email makes a lot more sense than an email client implementing text editing. Especially for mostly-text emails or emails discussing, say, code.
> calendar
This one is pretty workflow sensitive, but Org Mode encourages a very holistic approach of writing everything related to a project in one file, then parsing the file for dates and creating a calendar. If this is your workflow, again it makes more sense to implement from a text editor (because the "calendar" is really a parsed text file and maintaining the text file is what the user works on).
I can see a lot of utility in a stand-alone calendar program if the workflow you want isn't based on text, though.
> PDF
Has me stumped, although sometimes when I write documents that are going to be emailed as a pdf I'll use emacs and it makes a lot of sense to preview in place as I go. I must admit, the advantages aren't really there for me on this one, I prefer stand alone viewers.
> changing the window in focus
The secret is that many tasks involve 60% editing text and it then starts to make sense to implement the 40% in an environment where your heavily customised keyboard shortcuts all work. Eg, at the moment I'm writing a comment for a website - if I only viewed sites like Hacker News (mostly text reading and editing) then I would 100% end up doing it from emacs. Emacs falls down with images and navigating modern webpages though (haha modern; anything written in my lifetime), so I use a browser like everyone else.