You're assuming that'd be the case. Identity is a very individual thing in a your mileage may vary kind of way. Different people have different experiences.
Also, us Canadians and Americans have a very different experience because of the way our countries operate. Both Canada and the USandA have always applied Jus Soli to citizenship, meaning all you had to do was be born here to be a citizen. It didn't matter if your parents arrived in the country earlier that day. Many European countries don't have that. This was especially the case 15-20 years ago and earlier. Many people were born in Germany, even to German-born parents, and weren't citizens because their grandparents moved from Turkey or Serbia and the whole family were still considered Turkish or Serbian "guest workers" and therefore foreign nationals.
In some cases, you do have footballers who literally could not play for the country they were born in because they did not hold its citizenship(countries like Sweden and Germany also forbid dual citizenship), but you also have cases like Croatia's Ivan Klasnic, who's famous for coming back from two kidney transplants to score in the quarterfinals of the European championship. Klasnic wasn't born in Croatia, but in Germany to ethnic Croat parents. He held Croatian citizenship, but was offered German when he first burst onto the scene as a talented teenager. The offer, of course, had to do with the German football federation wanting him to play for Germany. He said no to both the passport and the German team, as he claimed he didn't feel German. Hard to argue with him, as he grew up being told by the German state that his family were temporary workers who were expected to return to Croatia(his parents aren't even from there, but from Bosnia) at some undefined future point and that they were not going to be granted citizenship because they were not ethnic Germans. I wouldn't feel very German either.
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