... there were no countries?

Imagine a world without any borders. You are born without a certain nationality. Your identification feature would only be your name. You could go wherever you want in the whole world and do not need to take care about restrictions from the government, like taxes for eg.

There would be no discrimination based on the fact where you are born. Would this not be a real positive impact on your life? Especially when you have a look at the political situation right now, thinking about the refugees, this seems quite compelling.
But would the problems actually be solved? And what are the actual positive effects of countries, that we would loose? For what reasons do countries exist?
If there would be no countries no one would be responsible in a greater extent, than his own surrounding, whether it is about people or the environment. Problems like climate change could not be approached. What happens to older or ill people? There would be no healthcare or retirement planning.
What about the educational system? Who would take care for the standard of knowledge and the chances that arise with it?
The whole infrastructure would suffer enormously. All the advantages of a bigger civilization would be lost. And what would happen to national features? There would be a loss of culture, specific knowledge, art, architecture, food etc .
It would actually be anarchy.
Countries are needed as an organization form and for the structure, that comes with it. In fact it is an achievement of human culture as long as it is not abused. With borders there come problems, but countries are the best working organization system right now, that humanity figured out.