"should" is a strong word. If you have a very short and fast HTML page you might want to start pushing the assets just in case the user doesn't have them cached. But yet, the choice is yours.

I wonder if the proxies would consider some sort of hybrid mode where they proactively fetch the link header and cache it (if it isn't already cached) but don't push it to the client. I can't find any indication that this has been implemented or considered anywhere. Of course if your edge was much closer to the user the the origin it wouldn't have much benefit. But it would still be nice.