I find it extremely hard to understand why nobles of a culture use bows while the rest of the people don't.
You could use that argument to say "I find it extremely hard to understand why nobles of the Empire use lances from horseback while the rest of the people don't".
Longbowmanship is something that takes a lifetime of training to master - Welsh archers were required to train weekly from the age of seven - and a lot of strength, and longbows were the absolute epitome of archery technology in the 1000s, requiring skilled bowyers to create something that could output so much force. They weren't widespread, until the English finally started training up their own longbowmen they were forced to hire Welsh ones because it isn't something anyone can just do easily.
With these barriers to entry that mean you have to train your whole life to become a longbowman, it's plausible that common recruits wouldn't be able to upgrade into longbowmen, only specialised elite ones.
Battania is an attack to common sense and historical facts.
I think the common sense argument is solid enough, as for historical facts, Battania is based on an assortment of Celtic peoples: the Ancient Celts (known for shock infantry), North Welsh (known for pikemen), South Welsh (known for skill with longbows), Irish (known for light javelineer skirmishers), and Scots/Picts (known for shock infantry).
Out of all Celts, only the South Welsh used bows in significant numbers. All other Celts favoured the javelin far more than the bow. The Irish almost didn't use bows at all until the Viking invasions, and even after that not in large numbers.
So Battania's current state well represents the historical use of longbow among Insular Celts as a cultural group; a small amount of them used it very well, the rest didn't really use it at all.
Luckily we have a fantasy environment.
Yes. Or ahistorical fiction/super-low-fantasy at any rate.