You are certainly taking the terms "global citizenship" and the term "globalisation" to extremes. Probably based on fear and paranoia.
No one is proposing to do away with countries. Being a global citizen merely means being respectful of people and countries, working/living together as brothers and sisters. Just being nice to each other really. It doesn't mean we should do away with countries and borders. That is a very extreme interpretation. Paranoia to the max!
A great sequence I took from an economics text is a pyramid that follows these steps.
1, Free trade area
2. Customs union
3. Common Market - Common Currency and free labor mobility,
4. Economic and Political Integration.
The EU has gotten the furthest, but this is the pathway for every nation. Politically, the US could not offer free labor mobility so instead it purposely allowed illegal immigration. The pathway is still there but Trump sort of blew this up. Trump is more of a nationalist. So he has some properties in other nations. He still puts America first. It looks like his tariffs will set nationalism back so far that many if not most Americans will fixate on free trade. I would say Trump is a free trade advocate worldwide, but instead he is mercantilist and seeks to accumulate an advantage to America. Regardless, if this experiment in tariffs fails the pendulum will swing to greater integration. Environmentalists generally seek global solutions, there are some calling for international taxes, and the special drawing right (SDR) is just one pathway to a currency that assimilates other national currencies.
In the court system, the US Supreme Court in 2005 sided with international law in Roper vs Simmons. This ruling was to forbid the USA from executing a juvenile criminal.
The best evidence I can cite is a survey taken around the world that asked people about global governance. Here is a quote from the abstract. Source:
https://academic.oup.com/isq/article/68/3/sqae105/7732859
"Specifications as democratic and/or focused on global issues like climate change significantly increase public support and lead overwhelming majorities worldwide to favor a global government. Support is even stronger in more populous, less free, less powerful, and/or less developed countries. The only exception is the United States, where no global government specification receives majoritarian public approval.
Overall, our findings show significant international support for fundamental transformations of global governance, and thus indicate to activists and policymakers that relevant reform efforts can build on widespread public endorsement."
You can believe what you want but the world is nearer and nearer to a more global system. Sure there can be borders and nation states, but the push is on for a universal set of human rights, greater precedence of international law, and more centralized power.