As I said, I suspect the "of country X" designations are mostly a feature of European monarchies, but I will leave that to someone with more knowledge of Asian and African customs. However, even in modern Europe, the princesses/princes of the Belgian nobility for example are formally "princes and princesses of nothing" (there are official sources for that
here).
We don't even have to go that far. Children of British sovereigns are "princes/princesses of nothing". Only Prince Philip, I think, is formally referred to in his LPs as "Prince of the United Kingdom". Otherwise, it is HRH The Prince Charles, HRH The Prince Andrew, HRH The Prince Edward, etc.
The way I see it, at least for the Brits, one thing is the
titular dignity of Prince/Princess that is prefixed to their Christian names under the LPs of 1917 and 2012 and a different thing are the titles that they were given by specific LPs applying to each of them individually and which are postponed to their Christian names. Hence,
HRH The Prince Charles (Philip Arthur George), Prince of Wales
HRH The Prince Andrew (Albert Christian Edward), Duke of York
HRH Prince William (Arthur Philip Louis), Duke of Cambridge
HRH The Prince of Wales, HRH The Duke of York or HRH The Duke of Cambridge are only short styles for daily use corresponding to the above in my point of view.
The Belgian system, always controversial here in TRF, is not different IMHO. The princes and princesses carry a titular dignity that is prefixed to their name, followed by their given names (and family names if used), their dynastic titles, and then the
title of Prince of Belgium when applicable. Hence
SAR la Princesse Élisabeth (
Thérèse Marie Hélène), Duchesse de Brabant, Princesse de Belgique
The only
main difference is that, in the UK, under the LPs of 1917 and 2012, HRH is attached to the prefix Prince/Princess, who is turn attached to the given names (it is a style that applies to ALL people entitled to be called Prince/Princess under the said LPs, regardless of any other title that they might hold).
Conversely, in Belgium, HRH is also prefixed to Prince/Princess and the given names, but it is attached to also holding the title of Prince/Princess of Belgium. Anna-Astrid for example is not a Princess of Belgium, and not an HRH accordingly, but nonetheless uses the prefix Princess before her name.
We don't know yet, but I believe that Nicolas' and Aymeric's children, or Louise's and Maria Laura's for that matter, will also be Princes/Princesses of nothing without an HRH and so will be all
legitimate descendants of Albert II in perpetuity as, that is my reading of the Royal Decree of 2015, but, again, we don't know that yet. Hopefully the Courts will clarify that in the context of Delphine's case.
Anyway, there are other examples too. Carl Gustaf's sisters, or Carl Gustaf's grandchildren other than Estelle and Oscar, are not HRHs, but are Princes/Princesses followed by their names only (and family name if they use it in their identity documents; for the sisters, followed by their husbands' names).
To me, "of country" is not the rule, but rather the exception, signifying membership of the Royal House (at least in some countries).