1&1 (Ionos) hosted Exchange 2013 mailbox works fine in Outlook and via Webmail but doesn't work on iPhone. The account gets added to iPhone Passwords and Accounts without any errors (using server exchange.ionos.eu), but when in the actual Mail app, no emails get ever downloaded, and occasionally it pops up an error saying that connection to the server failed.
The issue was caused by 10 mobile devices already present in the Exchange mailbox ActiveSync device list. Most of them were old devices that haven't synced with this mailbox in many years. To remove old devices open Outlook Web App and go to Options > Phone.