As a free-speech absolutist, the basic problem you should have with this is that as precedent, it would lead right into the legislature being able to force the press to publish certain things because not doing so would be 'censorship'.
In the hypothetical world, where press is a natural monopoly, we would be far less likely to allow the press to refuse to publish viewpoints they don't like. Or we would outright nationalize the press and lead to a different sort of problem.
I think this is a case where "free speech absolutism" is not perfectly aligned with "first amendment absolutism", but either is a logically consistent framework.
