I think the important thing about this "combo"--and as jotheonah notes, most people might not call it that but, frankly, I would think it is--is to look at the final outcome.
Best case: After playing Hamlet, no duplicates in hand. You get +1 action, +3 cards. That's the same as two Labs, or a Stables without the discard.
Next case: You have to discard a card. You get to choose between +2 actions, +2 cards--a Level 2 City--or +1 action, +1 buy, +2 cards--equivalent to a Worker's Village plus a Moat. But you get to choose between them--and you got to sift a card in the process.
Worst case: You have to discard two cards. You end with +2 actions, +1 buy, +1 card, equivalent to a Worker's Village. But you also got to sift two cards in the process, which could be huge. And to get forced into this, after playing Hamlet you need two pairs or a triple.
In other words, in many cases this is better than buying some of the better $5 cards out there.
Now, Menagerie can shine on its own with good trashing... but this gives Menagerie a chance without trashing, for only $2.
There's a reason Hamlet will likely be the best of the $2 cards when theory posts those, and Menagerie will likely be in the top 5 $3 cards. Combining them can be really big.