I work in both the Office 365 home world along with the Office 365 Business world, and wondering when they might give us the Outlook.com web interface as IMO its a better web UI experience.
I'm one who flip flops between the desktop apps and the web apps as I can't decide which one I really want to use. With PowerApps, Flow and SharePoint web apps, it seems like it makes more sense to just work within the web browser.
I don't seem them making a Windows Store app anytime soon for SharePoint, Teams or Flow. They have deprecated PowerApps, Delve and I think in the near future Sway.
I'm going to attempt this week to work only on the web versions. I want to see if I could actually do it. Because I'm kind of the old school with the desktop apps I don't have much faith that I will make it through the week with web only. With Skype for Business it will be tough as on the web version you can't make Skype calls and my organization is not really on Teams, plus my tenant hasn't been given where I could set my user to Teams only.
Since OWA is code from Exchange, and outlook.com is not, it will take a bit. Check the office 365 roadmap and you will see some items are on there to get ported over to the Exchange OWA. They are working on it and adding new features all the time.
With the new Exchange 2016 (or maybe 2019), the name was just changed from "OWA" (Outlook Web Access), to "OOW" (Outlook on the web). With the new Name Changed ,they spoke about how they are bringing new features over to that interface from the outlook.com interface. This has been months and months ago. Its best for you to google and search for some blogs so you can read about it. But, if you really want a feature added sooner than later, its always best if you go and post in UserVoice so others can also vote on your feature request. The more the votes, the faster Microsoft looks into it., Heck, who knows, the main feature/features you want might already be on UserVoice, so just go Vote on it