Up to about 3-4 months ago, I thought the Wii U was an expansion onto the Wii. Never seen any advertisements to it - never even seen it at someones house.
I feel the real problem with Nintendo is they have failed to keep up with the times and has fallen back, much like Blackberry in sticking with their 'roots'.
All the way up to the N64, everyone had a Nintendo, the next generation - Playstation 2 vs GameCube vs Microsoft, the games on the gamecube were subpar to its competition, very cartoon looking (which is not necessarily always a bad thing) while the others were going for more realistic which caught hte attention of the growing target audience.
Nintendo was still staying in the N64 era for games. It lost its appeal to the others. Sure, there are kids who would be interested, but if they have an older sibling/young father that enjoys gaming, they were probably looking at the Playstaiton or Xbox, which in turn persuaded the younger audience to what is 'cool'
As for the original post/title, there is no way I would think nor want Nintendo/PS to merge. Stay in your own backyard and keep the competition.... Until they have to change their strategy, which I feel it is going to be too late and they will only be a niche market player.
As for the gaming portion - I defintely would love to rock some of the emulator games on my PS4.