How to synchronize Internet Accounts from macOS with iOS

What I'm trying to achieve

As indicated in the Keychain FAQ, "iCloud Keychain can also keep the accounts you use in Mail, Contacts, Calendar, and Messages up to date across all of your Mac computers.". And I want it! 😎 To be specific, I want to synchronize the Accounts I have configured on my MacBook (macOS, see screenshot below) with my iPhone (iOS) so I can reuse the configured email accounts instead of having to setup all of the 6 accounts again on my iPhone.

Tech specs

• MacBook Air
  • 13-inch, Mid 2012
  • macOS Sierra - 10.12.2 (16C67)
• iPhone 7 plus

  iOS 10.2.1 (14D27)

What I've tried

I activated iCloud Keychain in macOS (see screenshot below). I would think that this is enough to make my Internet Accounts available for synchronization through iCloud.

Then I activated Keychain on my iPhone (see screenshot below). I would think this is what makes the Internet Accounts from iCloud available on my iOS device.

The problem

I think I setup everything properly (of course 😉) but I cannot figure out how to get my iPhone to show/use the Accounts I previously setup. All I get is this (in "Settings > Mail > Accounts"):

The questions

Hopefully somebody can tell me whether I'm doing something wrong, missing something or using a wrong approach. Or maybe I'm missing a screen/setting?

Thanks in advance! 🙂