Hi SamWu-MSFT,
"what is the version of the Contonso Web Server template? Only v1 and v2 templates are allowed in Web Enrollment Pages" - v4 (this time I've selected Windows Server 2016 on the template's properties page).
After re-issuing the template as v2 it did not appear in the template's list until I've granted Authentication Users the Read and the Enroll permissions, which I've never done before! So you were right - v4 don't work at all ALTHOUGH THE ARTICLE YOU MENTIONED ABOVE APPLIES ONLY TO Windows Server 2008/2012!!!
There's, however, one question left: why do the different templates show up differently on the Web Enrollment page?
In other words: why does the Web Server template not require the Authentication Users\Enroll permission while the copy (v2) of this template - Contoso Web Server does require? I'm requesting those certificates as domain\enterprise admin so theoretically I should NOT need the extra permission for the Authenticated Users group (and I've never done it before)?