The reason isn't strange:
Wales was conquered by England in the 13th century, thus removing Welsh as a nationality. Can't be a nationality if it isn't a nation.
Scotland unified with England in 1707 for financial reasons (England was a rich empire, Scotland was a poor little country with a ruined economy and needed bailing out big-time), thus removing English and Scottish as nationalities for the same reason.
However...
For the same reason, British isn't officially a nationality either. Britain isn't a nation because it's part of the UK (which is a nation). Yet 'British' is offically accepted as a nationality.
Applying the same standards would either mean that English, Scottish and Welsh are official nationalities or that British isn't either.
Not all strictly true. Yes Wales was over run by the English granted. Scotland never had a ruined economy, Scotland might not have had much of an economy to start with but the act of Union was made to give Scotland an equal playing field on the European stage. Under the act of Union the Scots have a right to a Scottish passport. The act of Union is about equality between all home nations.