You have to remember that country, nation and state are three different things, especially on an island which was invaded and occupied multiple times. Wales was never a single, unified independent state as England and Scotland were until 300 years ago (and Scotland hopefully shall be again), but there were petty Kingdoms within the territory before it was finally annexed by England around 450 years ago, and it is a distinct nation. Its culture and peoples were and are different from the others on the islands, and are effectively the last remnants of the Brittonic people (and that's why Welsh seems so crazy, it's a different language group altogether from English).
But that's a rabbit hole too far for this discussion. You could think of the Brittonic people as being analogous to the First Men in Game of Thrones perhaps.
Americans would have a terrible time pronouncing Welsh.