Well, nationalization plays a large part in the way we perceive a banking system. Think about 21st century United States banks vs. others in the world -- I'm thinking specifically of Swiss banks and their legendary solvency, privacy, and trustworthy branding. In contrast, nobody trusts the U.S. banking system anymore. Our brand is tarnished, so our central banks are seen as lower-class. Even smaller countries are trying to consolidate their holdings to local, nationalized banks so a collapse of the U.S. dollar won't ruin their economies.
I do not see how nationalism plays any part in the creation of Central banks. There has been a rise in the number of Central banks mainly due to economic growth and the realization that it is necessary to have an agency that can help the government in regulating various aspects of the economy to ensure financial growth and an increase in prosperity of people.
I would suggest that countries do not like the idea of money leaving their own country. So, as to combat that, central banks were opened to keep money "closer to home." I also support the reasoning of globalization.
I would say that the world has gotten more complex and more interconnected. Think about the world in 1900, compared to now. We have had two word wars and globalization. The world is such a different place. I can see why countries would want more control.
I think we can link this in with nationalism, but also I think we have to enter globalisation into the equation as well. It is a certainty that as our world has become more globalised, nations have needed to develop banking systems that are more sophisticated and more able to help the country negotiate an ever-more complex world of global finance.
Nationalism has been a surprisingly powerful force in the twentieth century -- a century in which (at least according to some people) nationalism was supposed to lose influence. (Think of the old Soviet Union, which was partly designed to dampen nationalistic passions.) Even the United Kingdom is less united than it once was, with Scotland demanding more and more autonomy. Thus, the more that nationalism flourishes, the more national banks there are likely to be.
The Twentieth century also saw the rise of powerful countries and "super power" countries, but many smaller countries didn't want to lose the sense of national identity that could come from having its own sense of monetary power and control over it. This creates some sense of autonomy, even in light of the interconnectedness of the worlds' economy.
One factor is that more countries in the world have gotten to be big enough and to have economies that are complex enough to need central banking. Another reason might be that many countries have seen the impact of a lack of central banking in history. They have seen that central banks can mitigate crises and therefore they decide that they, too, should have a central bank.
This is an interesting point. I suspect that there are many more central banks, because as the economy gets more complex, nations feel that they need a bank that would manage the country's currency, money supply and interest rates. It also shows that the government is getting stronger and bigger around the world.