This is down to cultural differences, which are rooted in differing theological perspectives on the proper use of the power of the state and, in particular, about the extent to which state power should be used to enforce moral behaviour.
The Catholic tradition is the more liberal. In a tradition that goes back to Thomas Aquinas and, before him, to Augustine, the predominant view is that the primary purpose of state power is to preserve social order and the well-being of the community (the “common good”). On this view, things should be prohibited only if the common good requires it. The mere fact that something is itself immoral is not a sufficient reason to ban it.
The Protestant tradition owes more to Luther and Calvin, who considered that the community should be Christian, and that the state as the emanation of the community should also be Christian and should reflect Christian ethical thinking in its laws. Thus the fact that particular behaviour was evil was a good reason for banning it.
Prostitution is the classic example of how this lines of thinking work out in practice. In the view of Thomas Aquinas, prostitution was inherently damaging to the community. But he shared the prevailing opinion of his time that, sinful and harmful as it was, prostitution provided a necessary outlet for the sexual energy of men who lacked the social or financial standing to become betrothed, and the moral fibre to practice chastity. There was a large class of young or poor men who, if they could not visit prostitutes, would tend to engage in more disruptive and harmful wrongs — rapes, seductions, debauches, threats to family, property and social relationships. This was worse, in his view, than the damage which resulted from the practice of prostitution. On balance, therefore, the common good required the state to accommodate prostitution.
Augustine’s reasoning was slightly different. but he arrived at the same conclusion. Laws, he felt, will not be respected or enforced unless they enjoy at least the assent, if not the active support, of a critical mass of the community (which, he considered, a ban on prostitution would not). It is damaging to society and to the rule of law to make laws which are not going to be respected or enforced. Therefore they should not be made.
Luther’s position is an interesting contrast. He was fully aware that laws attempting to legislate personal morality could not always be enforced, but he did not see this as an objection. To his mind, if prostitution, when criminalised, went on anyway, but underground — well, at least the state would not be complicit. This was better than the state appearing to condone immorality.
Calvin was even more strongly of this view, favouring the criminalisation not only of prostitution but also of adultery.
For Luther and Calvin, in other words, unworkability or unenforceability was not an objection. It was important that the law should say the right, moral thing, even if that did not result in the right, moral thing being done.
And this is why, to this day, prostitution is more likely to be criminalised in historically protestant countries, and regulated/licensed in historically Catholic countries.
The tension between these two approaches hasn’t gone away. If we think about debates over the legalisation of cannabis or other drugs, for example, there’s a reasonable group of people who accept that criminalisation has been ineffective to control or eliminate drug use and is likely to remain ineffective, but who are still queasy at the thought of legalisation because “it sends the wrong signal”. They may not know it, but they are channelling Martin Luther.