The only genres I really think benefit from it are FPS/TPS or adventure/rpg games with similar perspectives,You can make the case that they're not common because of the dual analogs, but given that even with the vita, shooters control pretty poorly, I think it's just not a genre suited to the medium.which tend not to be terribly common on handhelds.
I think they are not common in handhelds because there is no dual analogue on the 3DS. There are many, many games on the Vita that makes explicit use of the 2nd stick after all. Also, I don't think that specifically excluding entire genres of games that require the 2nd stick, then claiming that the 2nd stkicks are not important, really strengthens your argument.
Also, shooters control just fine on the vita from my experience. Not as good as a console controller, but it is better than any handheld before it. Freedom wars for instance has really strong shooter mechanics which are enjoyable. You can't tell me that monster hunting games are not suited for the handheld can you? Impossible to do on the 3DS due to the lack of a stick. Although maybe the new 3DS will have it.
TOTP: Buy Freedom Wars so we can get the sequel goddamit.