On deceiving the simple with plausible-sounding words

Seen today on the feed of a prominent Reformed Baptist ministry: 

Premise 1- Government must promote the public good
Premise 2- Christianity, as the only true religion, is part of the public good 
Conclusion- Government must promote Christianity as the only true religion

This conclusion does not at all follow, since (amongst other reasons, but we'll just go with this one for now) there is a disguised/missing premise which is also required:

Hidden Premise: It is the explicit duty of Government to promote any and all public goods (and actively suppress alternatives)

i.e. This argument collapses, or at least severely reduces, all concept of "sphere sovereignty". Must the government force children to do enough exercise, and actively interfere if they fail to? And why just children?

Once such a premise is admitted, both logic and actual human history tell us that there's no logical stopping place to hold back where it'll be taken to. Why just "promote Christianity as the only true religion", and why not "promote the correct specific form(s) of Christianity, and hinder others"? Is it only some vague, under-specified Christianity itself which is a public good, and not any doctrines or practices in particular?

And who will be deciding which ones are correct, by the way? I mean, as long as it's me, then things will turn out just fine, so, no worries there. But if it's you then I'm already quite worried, since I've observed that you sometimes fail to even manage yourself and your family correctly, so being the one true arbiter of all religion for the nation is certainly beyond you. Alright then, that observation applies to me too. Who's it going to be, then?

Oh, it'll be "the Bible", of course! But again - who will be adjudicating what is correct interpretation of the Bible? Is that me, or will it be you? For a start, since the apostles never teach us anything at all resembling the above syllogism, I think we're already off to a very bad start.

But, I suppose, you're going to propose some new version of a "mere Christianity", a minimal creed which the state will decree as acceptable, and it will promote that, and suppress the rest? The Trinity's in then, presumably. I hope, though, that this won't include Eternal Functional Subordination, or attributing three wills to God, and everyone who's dabbled with those will be suppressed? Good stuff. And as Christianity is defined by the gospel of justification by grace alone through faith alone, independently of needing the benefit of any ritual performance to be justified, and not merely by Trinitarianism (which even the demons believe, and tremble), then certainly Roman Catholics are out. The state has a duty to suppress the works of G K Chesterton and J R R Tolkien. Oh, you like those two? They're different? Well, we'd better have some kind of star chamber of the approved theologians to work all this out for us. Who's going to be on that, by the way? And... what will the state be doing to those unfortunate people who feel conscience-bound before God to promote the errors they believe? I mean, the mental vision of all recalcitrant promoters of incorrect eschatology being marched off to the gulags has a certain Je ne sais quoi to it (good job I'm not one and that only people I disagree with will be caught by these proposals!), but I'm wondering if that's exactly what you had in mind?

And so on and on and on we could go. In practice, in 2025, even generally healthy evangelical denominations have difficulty policing their boundaries. And yet, apparently some Reformed Baptists now think that not only should we allow the state to arbitrate doctrinal questions and what is and isn't inherent to the promotion or denial of true Christianity, but that it's actually required of it.

On the contrary, we should hold to the historical Baptist understanding that the state has been delegated limited authority from the triune God (which it would be better if it recognised, but whether it does or not) to deal with outward breaches of and promote obedience to the second table of the law, as well as to regulate all other necessary accompaniments of government itself, but that the promotion of Christianity is a task which the Great Commission handed explicitly, and only, to the church.

Ah well. It's clear, then, that the given syllogism is about as valid as this one is: 

Premise 1- Government must promote the public good
Premise 2- The historic Baptist position, as the revealed will of our Saviour in Scripture, is part of the public good 
Conclusion- Government must suppress all its competitors, including the invalid syllogism with which this post began