Cultures? People on one both sides of the border generally have different culture and hierarchies of values. Thanks to borders, every nation gets to organize their piece of earth as they see fit (at least in democracies).
And my point is that the idea of "their piece of earth" is outdated. Apart from silliness and unnecessary politicians it leads to real problems, like countries deciding that they will burn oil and coal on "their piece of earth" and not care about climate catastrophe at all.
Same e.g. for combatting tax evasion. Many other areas do not strictly require transnational collaboration, but it's immensely helpful. For example, the power network in Europe is incredibly resilient because it is shared across dozens of countries. So every individual failure is rather small, even if it takes a large nuclear power plant offline.
I love how these sort of bureaucratic things are so simple in the EU. For the rest of us, it is much more complex, and for most of us living in a country we like is a dream that can hardly be achieved. Nearly all my childhood friends living back home are trying to escape their country but it's not that easy (you need to find a job that accepts H1B for US, or equivalent bureaucratic mambo jambo for the EU).
Also note how many of your problems are exceptional. Few countries raise taxes from money that never enters or leaves their country, and military service requirements are often paused while you are abroad. You have it harder than most.
I really do believe that we have way too many governments, and borders are an artificial construct used to support politicians.
Personally I like that the world has both types of governments. It provides, to some extent anyways, redundancy against the failures of each type of government.
On top of that then come all sorts of historic, cultural, ... reasons to "protect" each other which have all complex reasoning. Power-hungry politicians are only a quite limited reasoning, as many borders are supported by societies (by far not all, though)
Borders are necessary because of power-hungry politicians: without borders, entire levels of governments would become unnecessary. This is why we hear so much about "patriotism" these days.