I do think that using EXAMINE and SEARCH as separate verbs makes gameplay a bit of a chore.
Essentially examine and search play the role of revealing something hidden, and if it is clear that SEARCH needs to be used sometimes, it forces the player into EXAMINE ing and SEARCH ing for every object in the game. I think it's reasonable to examine most objects once, to get a clue, but SEARCH ing is essentially a deeper examine, that may or may not have a custom response. It places a huge burden on the player to do everything twice.
MOVE, PUSH, PULL, TALK, SWIM, THROW, LIGHT, ... all of these are individual actions, but requiring a deep examine isn't really an act of creativity by the player. It just forces the player to type EXAMINE OBJECT then SEARCH OBJECT, and with some players not expecting to search at all.
I'll write something in the rules about this, but if you have a game that absolutely requires search, then it'll be permitted.