Support told me that's "normal", but I don't think so
"Greetings friend!
Thank you for contacting The Elder Scrolls Online Customer Support.
This is something I have noticed myself and have asked the very same questions. Usually in Elder Scrolls games the weapon buff visuals will be fully animated as long as the enchantment is active.
However in Elder Scrolls Online at the moment it is as you have described, the enchantment is visible for only a moment and then disappears. This is how it has been since the very early stages of the game and is how it was intended.
However I suspect this will be changed at a later stage as it is something that the fans would like to see and it makes sense to do it and keep with what has been established already."
Uh, what? What's the problem? That your sword doesn't get all flamy reliably?
Just saying, they still haven't resolved the fact that they are wiping out and resetting banks and losing character progress. No one knows how they are going to take action against the dupe bug and everything it injected into the economy either.
While annoying, I might put this on the back-burner..