I actually don't have a problem with this -- if MS wishes to build some functionality into Edge as the browser that ships with Windows, and then ship some apps that require Edge be installed, I don't really see any downside to that. Now, if they said you had to use Edge to visit certain websites, that would be bad, but this doesn't sound like that at all.
Having said that, I find the new Outlook to be completely unusable. It's missing many functions I need from Desktop Outlook, including Rules. But even beyond the advanced features, even the basic email editor is painful to use. In EVERY other program from MS (and most third parties too) the menu key on the keyboard and right-click on a red-underlined misspelled word brings up the menu to fix. New Outlook completely changes this. Also, in New Outlook, if you have a long list of folders, you can't drag and drop a message from the Inbox (or any other folder) to a folder that's not currently visible. You have to manually scroll the folder list first. This is also completely different and worse than how it works anywhere else where when you drag to the top of a list it scrolls down and drag to the bottom and the list scrolls up so you can drop in any folder.
These are just basic UI features that I am baffled MS has broken in New Outlook. I feel like I'm using Mac OS -- it looks fine, but is functionally painful.