For email: Two step authentication and poor web browser integration kept me from using the browser on the XB1 or PS4 for anything other than random stuff. It's actually easier for me to do the things you mentioned on my phone via the apps provided by my bank than it is to kick on the console and start working their browser software. Ease of use is a factor here.
For video editing: Can you really though? Could you have put together something on par with all of the submissions in the CTRL+ALT+SPACE contest? Could you have cut down and added a 20 second clip from a song out of your library? I too, can press a button on my controller and start recording everything the PS4 is putting on the screen, no matter what my current activity is. Console editing software isn't even on the same level as Microsoft Movie Maker.
This notion that console owners need to be able to do productivity work on their console is silliness. Email on a console? LOL, this isn't 1995. Most folks use their smartphones for email, along with video recording and editing and everything else listed. The reason a console is good at gaming is because it focuses on being good at gaming.
My PC is an older Macbook Pro (I had to go Mac for business reasons). It's terrific for all these productivity examples given. It's terrible for gaming. Hence, I own a PS4 for that. I would personally
never mix productivity and gaming on the same machine, primarily because I don't trust all the DRM mechanisms used by game developers (Ubisoft, I'm looking at you). Then again, I don't trust Windows in general with my personal data.
Email on a console.. HAHAHAHA!