Why wouldnt a catholic theocracy work
If this theocracy would instill Catholic religious and moral doctrine, it would not work. Especially the moral doctrine.
A government, ultimately, requires the support of its people. If the people do not support the government, then the government will eventually fall.
The only way it can hypothetically work is if you had a very large majority Catholic population and the government censored people in some form or another. You could also rule by violent force, but I am assuming most sane Catholics (and sane people) would not resort to violently oppressing innocent people. I believe I am quite safe in that assumption, but, given how philosophy works and the positions of some individuals, I tend to abandon assumptions based on what I believe to be sane.
If the population was not majority Catholic, like in the United States, then the government would not stand. Some of the moral traditions from the Church, such as that on contraception and abortion, are very hard to impossible to argue for outside of accepting other Catholic doctrines. In other words, unless you already are Catholic and accept orthodox teaching within the Church, the Church's stance on moral issues like abortion looks like Kant's ban on lying. This leads to a very upset populace. And this is simply on very specific area of morality. We have not gotten to religious freedom and other arguments for freedom of choice, among other matters. In other words, without a majority backing, the government will fall. People generally don't like being forced to live by a set of rules from a religion they do not believe in.
If the flow of information is not controlled and certain voices are not censored, the government will experience problems. When people have a voice, anyone with a decent amount of logic and rhetoric can convince someone of an opposing view. With the freedom of information, dissenters are going to rise. Eventually, things are going to turn out to be the situation above, or, at least, enough of the population is going to oppose theocracy on political grounds.
All of this is hypothetical, however. History seems to indicate that, even when there is a group of people of one religion and the theocracy has control over the flow of information, the government eventually breaks down due to strife. The power structure of the Middle Ages is an example.