Office 2013 completely falls apart on separate-DPI monitors. It's small on one screen and gigantic on the other, and doesn't automatically adjust as it should. It's more than just a few applications. The downsides of 4K don't really seem worth the benefits (if there are any).
I don't have that problem with Office 2016 and Windows 10.
Some old corners of Windows (e.g. Device Manager) are blurry and poorly scaled but that's about it. I never hit any real issues with my 4K monitor or its 1080p sidekick that I use in portrait.
That can't be true because every single app I've ever moved between monitors works fine and switches DPI, and I doubt every app has been updated for this.