Is it possible to have "toys played with" in the same vein as foods eaten per pet?
I don't personally see why, as (if I recall correctly) there is no achievement for playing with your pet with unique items. Also, you can play with your pet twice with the same toy, unlike, say, books, where you can only read them once.
Books - read once, reading achi Food - feed ∞, different food achi Toys - play ∞, no achi
doesn't need to be implemented, in my opinion.
Exactly -- I think it should be tied to a new achievement just like food.
I think this could make a really cute achievement. "is Playful" would also be a cute title that could be given with it.

I like the idea of having toy achievements. I think it would make items like hand puppets more … useful? I feel like they just sit around in user shops for quests most of the time.