If you remember back when Mario Kart was first released, there was a promotional offer on Club Nintendo where if you registered the game within the first few months, you could get a second game for free. These werent even small downloadable title, but full retail priced games. The four they had available were Wind Waker HD, Pikmin 3, NSMBU, and Wii Party U. I feel like since the NX is launching at such a weird time (practically the middle of gen 8) that having another deal like this would persuade more people to want to buy an NX. We already know that Nintendo is preparing a lot of big releases soon that will probably be tied to the NX (Zelda, Pikmin 4, supposed ports of Wii U games) so another deal like this where you buy one game and get another for free wouldnt be a bad idea. I doubt they will do this again though, but it would be nice.

Agree. Specially if they have a lot of remasters, they can just offer those as an incentive for buying the console the first year. Attractive to those that never bought a WiiU (which is a lot of people).

I have wanted this to be the case for Zelda U for a while now, I guess it works better for the NX as a whole.

I'm not sure what games will be available at launch, but let's assume that Splatoon and SMM are coming on top of Smash. Buy one, get one free. Sounds good to me. I'm not sure they would want you to be able to download their big guns (Zelda, Pikmin 4, 3D Mario) for free, if they do indeed release on launch.

I don't know if they necessarily "should" do it, but I definitely think that they would very smart to do it.

I don't see that happening but I can see Nintendo bundling the NX with a new game and a digital download for one of which ever games they decide to port from the Wii U (outside of Zelda U). 

There is no need for this at launch because people buy games at launch in any case and this way basically they would cut sales of some AAA game. Nintendo used this promotion in order to try to revive Wii U, NX does not need something like that at launch. Also, most likely NX will be bundled with some game.
IMO there is no chance that Nintendo will do this, not at launch at least.

Well, an offer that basically says that you get a new console plus one WiiU remaster game (Splatoon, Mario Maker or Smash are the best bets) and you might suddenly attract a decent chunk of people that otherwise wouldn't get it at launch. And they do need a great launch, at least to prove 3rd parties the interest on the hardware is there.

Maybe they could offer some Wii U ports becuse at end its just a port,  but I really don't see they offering some new AAA game like free game at launch.

With a lot of games getting price cuts due to Nintendo Selects, it would make sense!

Honestly if they have to go to stuff like this at launch, the NX is a flop anyway. The system should be enticing enough to sell itself at launch.