In Bridge, What is the Merit of Taking a "Double" Finesse?
You have answered your own question in the last paragraph. The simple finesse gets nothing because you can only win the Queen if the King is onside, in which case you will come to it in the end anyway, and taking it may consume an entry, lose a tempo, and so forth. 

In the second case you are, as you state, developing a possible long card, and (provided you put in the Ten) possibly the Queen as a winner if the Jack is right and the King wrong.