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.
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.
I can envision a scenario such as a REPL for PDF. If you write a lot of latex(or whatever format), it could potentially get converted to PDF and be shown right in your editor.
For document modes (latex and markdown) I have F9 bound to a function which invokes `make` if there's a `Makefile`, `nix-build` if there's a `default.nix` or `render.sh` if that exists. It then runs `killall -HUP mupdf-x11 || true` to force any mupdf instances to refresh.
Whilst I like to do things like email in Emacs so I can have the same powerful editing capabilities with the same keymappings, PDFs can't really be edited so there's not much incentive there.
Unfortunately, it lacks a continuous scrolling mode.
Moreover, I don't think that you can do something like manage your to-do list and reference an email directly between different applications but you can do that inside Emacs. This way I don't need to first search inside another email application which email I'm referencing to inside of that to-do list item.
I guess at the end of the day it just boils down to use whatever fits the job perfectly, whether it's combining different applications or use everything inside Emacs. Whatever makes you more productive.
I do wish there was a modern tool to replace Emacs. I thought it would be Squeak. Maybe it will be VSCode.