> Is the server somehow unable to inject an ID if the sender did not send one?

Yes. https://www.rfc-editor.org/rfc/rfc2821#section-6.3 refers to servers that do this and says very clearly:

    These changes MUST NOT be applied by an SMTP server that
       provides an intermediate relay function.

> Stop hiding behind policy and think for yourself.

Sometimes you should think for yourself, but sometimes, and friend let me tell you this is one of those times, you should take some time to read all of the things that other people have thought about a subject, especially when that subject is as big and old as email.

There is no good reason viva couldn't make a Message-ID, but there's a good reason to believe they can't handle delivery status notifications, and if they can't do that, they are causing bigger problems than just this.