Why dont Shaco's W or R boxes proc thunderlorda, deathfire touch, or spelltheifs edge passive?

E doesn't proc them either. I believe this falls under "hidden power".

Because that would be stupid and broken, that's why.

If Teemo's shrooms proc Thunderlords/DFT/Spellthiefs, it stands to reason that Shaco's boxes should proc them as well, since they're both the same category of summon.

If it turns out that Shaco boxes are coded as minions, then Malz Voidlings also proc those things, so Shaco boxes should as well. Riot just hasn't gotten around to updating the code.