- assign copyright to the publisher, have your work paywalled and pay for the access to it via exorbitant subscription fees the university pays
- ask for having it available as open access - and then the publisher charges you thousands of USD/Euro ($4000 is common) for the privilege as a condition of having it published.
Very few university departments can afford to pay such fees so you can guess where the papers end up.
And if you mean open access journals that don't demand these fees - well, that's of little use to an average researcher when their career depends on peer reviewed publications in reputable journals. Publishing it wherever, in a journal nobody heard about with who knows who doing the reviews has zero value and you won't get any credit for that.
Or, perhaps the different agencies can create their own journals for their funded projects and let the research appear in them? Basically, create new reputable journals precisely for open access? Or make it where a paper has to be submitted to a "prestigious" one and an open access one a year or so later (i.e. author keeps copyright, period), which would hopefully build up the prestige of them?
I'm not sure the solution, just trying to think of ideas.
As it stands, I'm fully behind Sci-Hub simply because I'm not affiliated with an academic library, and can't afford to pay all their damn fees. It harms individual researchers as well as individuals who are just plain interested in the material.