The great imaginary bugaboo is some Hitlerian anti-truth regime, but this is mostly a hypothetical. What we have now in this dead Republic is against truth at its most basic core, because the truth is someone owns something, and the thieves get together and pass a law to take from that someone and divide the spoils.
So, a real regime would have private property. A monarch would have a private property interest in his realm in the same fashion as farmer would have a property interest in his farm.
Already we can see freedom of speech would allow people to say this is not so. So truth loses out. Not just for the monarch, but for the farmer. Even in such a small arena of property rights, much garbage can be spewed.
Additionally, under the current situation, people actually think they have some sort of hold over others. They think, for instance, that you can trespass in order to engage in speech. And that another person actually has some requirement to stay, and listen to whatever nonsense you happen to be spewing at the time. So, it is not totally clear to me that we would have to do away with freedom of speech, if this erroneous assumption were quickly brought to an end.
Because, like I mentioned, if the king owns the realm, the farmer owns his lands, you are some progressive idiot, they can just kick you ought for trespassing if you won't shut up.
There are, of course, many more discourses to have, so barring tiring old redistributionist schemes, the likelihood is that speech would be relatively free in a society more concerned with truth, but that at a certain level ideas would be more rigorously tested, and multi-billion dollar global fraudulent schemes, like the multi-decade attempt to institute a carbon market, would not be able to happen. Funding for research would be more decentralized, though presumably, one could imagine a realm small enough in which only the king was the major funder of research. If this were to be the case, then there would also be all public research published outside of the realm, plus whatever the king consented to fund. A king, having an interest in the care and upkeep of his own realm, would consent to lines of research in the hopes of improving his realm and/or his own self. So, for instance, I could easily see a desperately ill king having as much research as possible done on his illness, or a relatively healthy king having research done on traffic flow. What I cannot see is Al Gorius the first, and his complicated schemes for power. A king already has power, and he would not be able to increase his power by perverting climatology.
A curtailment of speech then, is not necessarily a curtailment of truth. Indeed, a reduction of speech would likely, on the whole, increase the likelihood one would happen upon truth, should truth continue to be within the realm of acceptable speech. Of course, herein lies the problem, and the liberal would seize upon this and suggest that all curtailment of speech is necessarily evil- except perhaps whatever curtailment of speech the social justice warriors have dreamed up today.
But as we've seen, a curtailment of speech based on property rights is not an arbitrary approach, but an organic one, in which the environment in which you speak is respected. Additionally, if one were to raise the stakes surrounding speech what would result is less bullshit, not less truth.
Of course, as we have seen, the people most likely to destroy freedom of speech are the idiots I've used as examples in this post.