I suspect it’s more of a problem with them in practice than with the idealized versions of them (though I am not sure). For example, I can come up with a couple reasonable sounding Catholic theocracies (including a fairly week one, where you have a government that’s chosen by secular means as it is now, but where a the bishops of the country have collective veto power, and perhaps a few positive powers as well), and in an idealized society where everyone works for good (or at least good as they see it) and not for things like personal power, that would probably work.
But in actual society, what this would do is cause people to seek office in the Church for political reasons. A bishop ought to be a bishop because he wants to serve God, not because he wants temporal power, and the more temporal power a bishop has, the more likely you’ll have people seeking the office for the wrong reasons. We’ve had issues like that before. And so the corruption that always happens in government would seep into that into Church leadership. (Of course, things are never perfect with Church leaders either, but this would certainly exacerbate the problem.)
There are other issues as well - any real or perceived evil done by the (theocratic) government would be used as an excuse to attack the faith. We see this already, when people (sometimes justly, sometimes not) blame some of the evil done in the past on the Church at that time. Of course, the answer is that people aren’t perfect, and don’t magically become so when ordained and so still do evil, and that this doesn’t actually say anything about the truth of the faith they practice, but nevertheless there will be those who say “how could the Church do X if it were really what it claims to be?”
And then there is the problem that there are always those that don’t really support religious freedom, and all guarantees aside would work to force their religion on others. Of course, we have some of those in the government who don’t respect religious freedom already, but there’d be a whole new set of problems if we ended up with people trying to unjustly force what was actually right - it could easily interfere with both the governmental function and the religious function such a hypothetical Church-state would have. And similar.
I tried to find some sources on the subject, and ran into vatican.va/holy_father/benedict_xvi/encyclicals/documents/hf_ben-xvi_enc_20051225_deus-caritas-est_en.html from Pope Emeritus Benedict. About 2/3 of the way down:
a) The just ordering of society and the State is a central responsibility of politics. As Augustine once said, a State which is not governed according to justice would be just a bunch of thieves: “Remota itaque iustitia quid sunt regna nisi magna latrocinia?”. Fundamental to Christianity is … in other words, the distinction between Church and State, or, as the Second Vatican Council puts it, the autonomy of the temporal sphere. The State may not impose religion, yet it must guarantee religious freedom and harmony between the followers of different religions. For her part, the Church, as the social expression of Christian faith, has a proper independence and is structured on the basis of her faith as a community which the State must recognize. The two spheres are distinct, yet always interrelated.
Justice is both the aim and the intrinsic criterion of all politics. … But this presupposes an even more radical question: what is justice? The problem is one of practical reason; but if reason is to be exercised properly, it must undergo constant purification, since it can never be completely free of the danger of a certain ethical blindness caused by the dazzling effect of power and special interests.
Here politics and faith meet. Faith by its specific nature is an encounter with the living God—an encounter opening up new horizons extending beyond the sphere of reason. But it is also a purifying force for reason itself. From God’s standpoint, faith liberates reason from its blind spots and therefore helps it to be ever more fully itself. Faith enables reason to do its work more effectively and to see its proper object more clearly. This is where Catholic social doctrine has its place: it has no intention of giving the Church power over the State. Even less is it an attempt to impose on those who do not share the faith ways of thinking and modes of conduct proper to faith. Its aim is simply to help purify reason and to contribute, here and now, to the acknowledgment and attainment of what is just.
The Church cannot and must not take upon herself the political battle to bring about the most just society possible. She cannot and must not replace the State. Yet at the same time she cannot and must not remain on the sidelines in the fight for justice. She has to play her part through rational argument and she has to reawaken the spiritual energy without which justice, which always demands sacrifice, cannot prevail and prosper. A just society must be the achievement of politics, not of the Church. Yet the promotion of justice through efforts to bring about openness of mind and will to the demands of the common good is something which concerns the Church deeply.
Those "…"s are unfortunate, the whole thing is worth reading, but there’s a character limit. I’m not sure this actually forbids a carefully made theocracy, but even so, I think the practical problems with carrying it out would make it pretty much impossible to justify.