The simulacrum is by definition an NPC (since it is obviously not a PC). That said, the spell clearly defines your level of control over the simulacrum.
However, there is no RAW reason that a simulacrum cannot cast Wish. Wish is "the mightiest spell a mortal creature can cast." Meaning that if you are mortal, Wish is the maximum limit. It does not mean that you must be mortal in order to cast Wish. For example, genies are not mortal but some can nonetheless cast Wish.
Personally, I treat the simulacrum as if it were the caster for purposes of casting spells. Meaning that if the simulacrum casts Simulacrum it will cease to be (because it is treated as being you, and you cannot have more than one Simulacrum at a time). It also means that you can't circumvent the 33% chance by having your simulacrum cast a non-standard Wish for you (although I don't have that result in automatic inability to be unable to cast Wish again; rather, your monkeying with the fabric of reality has resulted in the forces of Law taking notice who will be sending an Inevitable who will seek to resolve the situation which could result in a quest or the loss of Wish).
Ultimately though, what the DM says, goes.