Warriors and desires being two syllables just sounds wrong, but til
That's because it depends on how you pronounce it. War-ri-or (wawr-ee-er_), or war-rior (wawr-yer). Oxford Dictionary suggests the first option when you google it, while Mirriam Webster uses the latter.
I'm not really a Pokemon person, but doesn't the presence of all those badges actually indicate that Soldier's an actually good Pokemon trainer?
Soldier very famously has never been in the army and has never participated in any war. All of the medals he earned, he made (and named) himself. Not much of a stretch to think he invented his own gym badges.