I have a feeling this will be another "no APU in the PS4/Xbone" type of post. And yes please give sources to your "extremely" everything surrounding HBM.
HBM isn't logical for the next Nintendo console considering what kind of GPU do you need to pair with a 500GB/sec+ memory bandwidth? By today's standards, a flagship one with 600mm2 die size.
XB1 only has 68GB/sec of native GDDR5 bandwidth, 768 shaders. PS4 has 176GB/sec native GDDR5 and 1152 shaders but we aren't seeing games on PS4 that look 50% better than on XB1. That's because the bottleneck isn't just the GPU performance but also CPU performance. For Nintendo to make a significant leap over PS4 then, it'll need to have a CPU 50%+ faster and GPU 50%+ faster, but the problem with that if 50-60 million XB1/PS4 consoles are weaker than NX, developers won't spend much money and effort taking advantage of NX's superior hardware. In essence, it would be akin to Nintendo making a powerful console only for themselves which they would not do.
Even if NX had hardware 3X more powerful than PS4, it would end up like Dreamcast which is way more powerful than old gen consoles but not powerful enough for a true next gen console. Nintendo just needs something from 2016-2021 and there isn't much point in making a console more powerful than PS4 since PS5 is probably not going to launch until 2019-2020.
If they can get backwards compatibility in play, that would be a huge plus. All those gamers who never owned Wii or Wii U would be able to play all the gems on the new console. The 2 biggest obstacles Nintendo has are 3rd party support and online gaming.
Also, right now we are just speculating that NX will launch in 2016 but it could be announced in 2016 and launched Q1 2017 which means 14nm/16nm design is still a possibility.
From an engineering standpoint HBM (well really HBM2) makes sense from the perspective that it creates a huge reduction in circuit board traces if it's the only memory type the NX goes with. This is especially more if the APU is an off the shelf type AMD is using in the PC world. As long as the whole APU + HBM2 doesn't get too hot, having all the heat localized to one spot will require a less substantial cooling unit as far as total volume of that unit goes.
Pretty much the smartest thing Nintendo could do when going to AMD was asking what AMD had in the pipeline and if it would be a fit for the NX, without having to create new silicon.
But you are not looking at the big picture:
1) Modern consoles are not PCB constrained. In other words, there is little incentive to use HBM to cut down on the PCB since the cost of HBM and its lower yields offset any advantages you get in reducing the PCB complexity/size.
2) HBM1 is limited to 4GB of memory which is less than PS4/XB1. Looking at how horribly unoptimized modern games are when it comes to their usage of VRAM, a 4GB HBM1 console going against 8GB GDDR5 would lose. HBM2 is too far out unless Nintendo gets 1st dibs even over AMD's own GPUs.
3) HBM1 and especially HBM2 provide so much bandwidth that it would be almost wasteful to pair them with a low end GPU like an HD7950/GTX960 at this time given how expensive and scarce it is. In the GPU space where say 30-50W extra power headroom and memory controller size reduction allowed AMD to go wider (600mm2), this benefit doesn't exist for Nintendo since they wouldn't use a 600mm2 GPU inside the NX.
4) You aren't addressing the CPU vs. GPU balance. Even if hypothetically Nintendo used a 4000 shader 600mm2 HBM2 GPU, what kind of a CPU would they need to pair it with? It won't work. XB1/PS4 are already CPU bottlenecked and pairing an even faster GPU with slow Jaguar cores is just a waste of GPU horsepower.
Nintendo may want to incorporate Wii/Wii U hardware for backwards compatibility and/or add a custom ARM core so that NX's games can play their handheld games too. All of that will just keep eating into their APU size leaving less room for a very powerful GPU that benefits from HBM.
Also, it's probably likely Nintendo is going APU route since it's the most cost effective solution for consoles today.
Finally, the most important aspect is that even if NX were 3 or 4X more powerful than PS4, who would make next generation games for it when 99% of the market is comprised of XB1 and PS4? No one! It would be a colossal waste of $ to make a powerful NX console.