A few thoughts:
People are acting as if Nintendo had already announced the NX launch for holiday 2016 and have delayed it. This was never the case, and for all we know they had always planned a March 2017 launch. Furthermore, a holiday launch isn't a necessary or sufficient condition for a console to be successful. Case in point: the Wii U had a worldwide holiday launch. There are any number of potential reasons (both in terms of hardware and software) why a March 2017 launch might be more favourable to Nintendo, and we have no idea what any of them are. Contrary to what many people would like to believe, Nintendo isn't staffed entirely with gawk-eyed morons who choose release dates by throwing darts at a calendar. They're a multi-billion dollar company who research every minute implication of a decision like this before going forward with it.
Aside from that, the decision not to show NX at E3 is a strange one, but there may be a few different reasons for it, off the top of my head:
1. NX isn't ready to show at E3
I think we can throw this one out of the way pretty quickly. The Wii U was playable at E3 almost a year and a half before release. This is 10 months before release, and they could certainly show off a handful of games, even if they leave more unveils for post-E3 directs.
2. They simply don't think E3 is the best place to reveal a new console
This is what I'd put my money on. Why reveal your new console within the few days of the year when you
don't get near 100% of the gaming media coverage? Nintendo have been moving away from an E3-centric PR schedule for a few years now, with more games announced throughout the year during Nintendo Directs where they can have a lot more space to themselves. Furthermore, with PS4K, PSVR and perhaps an XBO revision due at E3, they don't even get the exclusive "new hardware" coverage. In a modern, internet-driven world, it makes a lot more sense to have your own reveal show in your own time, when you can dominate the news cycle.
And if you still think that every console has to be revealed at E3, consider this:
neither PS4 nor XBO were revealed at E3. In both cases Sony and MS decided they were better off having their own reveal show than sharing the stage at E3. Now, both of these were pre-E3, but both consoles were scheduled for holiday launches. With a March launch the optimal reveal time may well be post-E3.
3. They want to wait until after the PS4K reveal so they can adjust their strategy if necessary
I wouldn't see this as being the main reason behind skipping E3, but in combination with point 2 it might make sense. They may want to adapt how they present the hardware, what their pricing strategy is, and other aspects of their reveal and pre-launch campaign in order to best position themselves in the market.
In a more unlikely scenario, they may wish to even adapt their hardware slightly to respond to PS4K. There won't be any chance of wholesale changes, as the SoC would already be taping out around now, but they could make a few more minor adaptations if they really felt it necessary. A simple example would be increasing clock speeds to squeeze more out of the SoC (as MS did with XBO pre-launch). If Nintendo had been targeting, let's say performance in between XBO and PS4 in a small, low TDP console, they may be able to switch to a larger case and a more capable power supply and cooling system and push up the clock speeds to match or even slightly exceed PS4 performance. Another possibility is to increase the RAM quantity, which can be done quite late on (as Sony did with PS4). With PS4K seemingly limited to 8GB of RAM, Nintendo may decide to move up to 12GB or even 16GB to have at least one spec where they can trumpet their hardware as superior.
The most unlikely possibility, although still theoretically an option, is to enable the full number of CUs on their SoC. I would assume that, like on the PS4 and XBO SoCs, AMD and Nintendo will have intended to leave two or more CUs disabled to increase yields. Enabling these two (or more) CUs could give them a performance boost, but would leave them with a higher cost per chip due to the decreased yields. As I say, it's a very unlikely option, due to the added cost, but it's technically available to Nintendo if they decide that PS4K's existence forces them to squeeze as much as humanly possible out of their already-designed chip.
Separate from all of the above, this does slightly increase the likelihood of a 14nm SoC in the console. I'd still count it as pretty damn unlikely, but it's perhaps a little more likely now.
Another interesting thing to consider is that if Nintendo's
entire E3 2016 floor presence is dedicated to Zelda, then that would be by a huge margin the most E3 floor space ever dedicated to a single game, and the game it's dedicated to is one of NX's big launch titles. It'll be a little strange showing it off running on Wii U after the NX version has already been announced, but it makes a bit more sense than having the first game they show off running on NX hardware being a last-gen port.