Important: S/MIME in Outlook for iOS is now available. The below article has been replaced by product content found at http://aka.ms/omsmime
Secure/Multipurpose Internet Mail Extension (S/MIME)...
Updated Dec 19, 2023
Version 13.0
Blog Post
After RTW answering my own question above for outlook on iOS:
For S/MIME verification (certifying the sender identity) it is enough to just have the S/MIME setting activated. There is no need to install a own S/MIME certificate on the device. The certificate is just needed for E-Mail encryption.
What I can also commit after my tests is - that S/MIME verification just works for O365 accounts in Outlook iOS mobile. Free hotmail/outlook or any other e-mail accounts don't do the S/MIME verification and just attach the digital signature as smime.p7m attachment - which you can not open.
I agree that at least S/MIME verification for all kind of e-mail accounts would be a great security boost for the fight against phishing and fraud mails...