Why don't Yen and Yuan add an 's' in the plural form?
Solution 1:
As noted in multiple comments, the premise of your question is faulty. Officially, the plural of Euro is Euro:
In Community legislative acts the plural forms of euro and cent are spelled without the s, notwithstanding normal English usage.
Solution 2:
Because Japanese deviated from the paths of English, Spanish, etc. a very long time ago, and thus evolved in a completely different direction, one that apparently does not include the suffix -s.