A hybrid PS4 could bring limited short and middle term benefits, as it would come when PS4 exclusively home user base is already large , and it would deny the novelty benefit to a possible hybrid PS5.
Moreover, even with a die shrink, the architecture used in PS4 APU is a lot less efficient than what will be available for PS5, and considering that during mobile use, disabling some optional OS services, only the CPU cores should work almost at their full power to give the same gameplay, while GPU cores could work at a greatly lower power or even be turned off while proper mobile ones would do their job instead, it's quite likely that a hybrid PS5 would be more viable and easier to design and produce than a PS4 one.
Also, without recompiling, every game using a graphics engine with a scalability range not large enough, or simply set to not offer such range even if the engine offered it in theory, probably couldn't run in portable mode in the worst case, or in less serious cases they could use too much power, making battery autonomy very unsatisfactory.
BTW, also on PS5, a hybrid version will be not only possible, but also viable, only if PS5 won't be released too early, as even considering current Jaguar cores are quite lightweight, only CPU cores using AMD architectures planned for late 2020 or later will be powerful enough even in mobile versions (or in mobile mode in hybrid APUs) to offer a performance leap from Jaguar large enough for a new generation of consoles. Luckily this latter problem will happen only once, when a new console will offer a hybrid version for the first time, as for the first time a lower CPU power consumption will be required too since the start, but from then on the successive console generations will greatly benefit from fast mobile CPU development, this could help balancing out the difficulties that are predicted to increase performances further as silicon tech gets closer to its physical limits at least for a while, although producers won't have to sit idle, but they'll have to use this extra time to plan a smoother transition to new techs.
Last but not least, if Sony and MS too will include a hybrid, this will slow down for the next generation switch the growth of resource requirements, and this could help many mid and small-sized SW houses currently struggling with fast dev costs growth to catch up with it.

It appears Nintendo chose the Tegra 1 over cost. Supposedly nVidia gave them a sweetheart of a deal on them. I suspect the Wii and Wii U also had their power plants chosen over cost.

I gotta say your response doesn't make much sense to me. The PS4 slim has a power draw of 165 watts. The new 14 nm Ryzen APUs have a power draw of 40-65 Watts. The switch uses 11 Watts when docked, 7-9 when undocked, and even then it's battery life is considered barely acceptable by even some of the most die hard Nintendo fans.

So how do we bridge that gap ? Sure we can use superior battery technology that is able to feed something like a 65W APU for 3 hours, but remember this thing is a handheld and needs a themal managemt solution that's probably going to be an inch thick or less. Maybe instead we go with a smaller chip with a lower power consumption, but then we have to start discussing the cost of shrinking such an APU down to a point where it has a more managable power draw, if its even possible.

It just seems to me that you're grossly oversimplifying your approach to this, and glossing over the fair criticisms that people are bringing up.

No point atm. PS4 is killing it. Why mess with a formula that is working so perfect for the atm.

Not everything needs t be portable lol

Depends where you are from, though. Console gaming is on a sharp decline in Japan, and I'm sure Sony is well aware that the future of console gaming is uncertain.

Here's what I'd like to see happen:

In recent years game development has streamlined so much that developers are making games and releasing them on all platforms without much hassle. A part of me feels as though game "generations" will be a thing of the past, and we will instead begin seeing consoles that receive yearly or bi-yearly upgrades that allow reverse compatibility up to a certain point. Sort of like what Apple does.

Sony could release the PS5, but instead of calling it a PS5, it could be a "reboot" of sorts, where it's just simply known as a PlayStation again. The following year they could release a more powerful PlayStation that games could take advantage of. At some point Sony would be able to create a portable version that trails a few years behind in terms of power, but still plays the same games.

I haven't given this a whole lot of thought, but in short, console manufacturers could begin creating their consoles such that they will be reverse compatible with everything before them, thus not alienating an existing user base.

Indeed. Cost may have been a factor. But they still could have opted for a Pascal powered chip for a minimal cost.

As for the Wii and Wii U, cost would have been a massive factor in the decision to opt for those chips.

The Ryzen APU's go lower than 40w.
You are making the mistake of looking at the desktop chips and thinking that is a representation of a Ryzen implementation in other form factors, it's not.
https://en.wikipedia.org/wiki/Zen_(microarchitecture)#Mobile_APUs

The power reduction can be taken even farther than that too.

I'm not suggesting to use a chip with a high power consumption or to shrink it.

False I have asked people to do their research.

How do you know the price difference would have been minimal?

Where are all those smartphones and tablets with a superior Pascal-SoC? With a competitive price, size and TDP there should exist some products in small form factors by now. 

How do I know? Because architecturally it's not a massive overhaul from Tegra X1. But it does clock higher, it is built on a better fabrication process and does have a couple of extra tricks like enhanced delta colour compression.

As for why Smartphones and Tablets don't use the "superior" Pascal Soc? Well. To be blunt... No one uses nVidia anymore in the Tablet/Smartphone space anymore anyway.
It's very much dominated by Qualcomm... With vertically integrated manufacturers opting for their own solutions like Apple with it's AX line, Samsung with Exynos, Huawei with Kirin... And then you have the likes of Allwinner, Mediatek and Rockchip bringing up the budget rear.

In short... nVidia exited the Phone market entirely as the profit margins and design wins just weren't happening... And has served the declining tablet market with older, outdated designs.
Thus they refocused there efforts on more specialized markets such as Cars, IoT and so on.

"Not a massive overhaul" doesn't mean that the price is similar. As you say yourself, Tegra X1 wasn't/isn't very popular for smartphones and tablets. So Nvidia was very interested to get a buyers for these SoCs to clear their stock. They probably made Nintendo a good deal for the TX1-SoCs.   

Yeah, they refocused their Tegra efforts on the much more profitable specialized car market. Car manufacturers don't have any problems to pay much higher prices for these SoCs... they multiply these costs for their customers anyways and make lots of profits from these "extras".

If Nintendo had said in 2015 (when they were planning the Switch) or in 2016 (when they were manufacturing the Switch) "We want the Tegra X2 instead of the Tegra X1", Nvidias first answer would have been "We are not offering the TX2 for these small form factors, they go in cars and we have more than enough orders for them." If Nintendo insisted, the second answer would have been: "Sure, if you pay as much for them as the car manufacturers. But for the Tegra X1 we can make you a much better price."

Again, you have no proof whatsoever that the price difference for Nintendo would only have been "minimal".

I find it hard to believe that a portable PS4 would even have a competitive price point against a $300 Switch. Plus what would I do with all my physical games? If the console is a bit too big, then it would be a bit inconvenient.

I really hope not