Two problems though.

1. Sony is a hardware manufacturer, and they have devices and knowledge in each of the markets I mentioned above. Currently they are using Android on these devices, and it is doing massive damage to the Sony name. They need to bring all of their devices onto a single Sony OS, and the PS4 OS is the best they have. By running the PS4 OS, and Using PS4 tech in all Sony device, they greatly expand their userbase, and make the PS4 hardware, PS4 OS, and PSN a much more lucrative place for developers, which in turn makes it a more lucrative place for consumers.

2. Streaming is the future, eventually, but it is not their yet. Data caps are real, and Remote Play + PS Vue + PS Video + PS Music + PS Now, is more than the average consumer can handle on their data plan. Even as a hardcore data user, it is not feasible. I pay $300 a month for data, and I have Unlimited at home, but only 50GB on Mobile.

I already use Remote Play a lot on the Vita, and it is good at times, but for some games, fighting and racing most notably, local is the only way.

This is a lot different than steam machines. Steam Machines has a bunch of different devices that were all nearly the same, and only focused on one market. 

What I am talking about is bringing PS4 tech to many different sectors, and using it to replace the current devices Sony already makes, in an effort to unify the company, and drive up profits. Sony is forcasting 12M TVs, 17M Smartphones, and 20M PS4s this year, in my example, that would be 49M new PS4 owners this year.

Seriously, this is the only logical way forward for them. They have to unifiy around an in house OS that drives up the value of their brand, and makes their hardware amoung the most lucrative places to release software, games, video, apps, etc.

Nah, my sig prediction is probably a lot more realistic. That said, I still don't think it will sell 110 million or more lifetime...

How many do you think it will sell lifetime?

Hard to say, depends on the Pro, how the Xbox brand will do in NA for the remainder of the gen, pricing strategy etc. but 100 million should be within reason. With around half that after three years on the market, it would need to sell the same for another three years to get to 100 million fast, factor in a decline unlike the PS3 and 360's unusually late peak due to unique circumstances on the market and ushering of the HD era on consoles and TV and what is likely to be a shorter gen than the last with a steep drop-off once new hardware is made available, and 100 million is a fairly reasonable prediction in my opinion. One could argue that the market hasn't changed that much, the problem with that statement is the relative lack of momentum for the PS4 despite its utter dominance over two main competitors; there should be more room for faster sales according to historical trends, but there doesn't seem to be that much, one console is down and out, or even DOA, and the other is only now selling decent amounts in one major market but slightly flailing globally. The PS4 has, so far, not outsold the PS3's best year by any big margin, which is quite telling given the above factors and the PS3's rather poor start (2015 saw the PS4 sell about 15-17% more than the PS3's best year, the PS3 was a third place console for most of the gen).

In short; with positive press, good pricing, some good software, great functionality and weak competition thus far, the conditions should be more or less optimal for the PS4, yet it hasn't really taken off in the manner that many expected. I still remember how ridiculous many thought I was being when I said that I don't think it will ever have a 20 million selling year. I can still be wrong on most fronts, but so far it seems to be proceeding pretty much as expected.

50M after their 3rd year - that's what all the PS consoles do, not just the PS3. And it doesn't need to sell the same over the next 3 years - it can do it over the next 5 years.

The best fiscal year sales for the PS3 was 16.5M with the 2nd one being 14.3M. The PS4 did 17.7M in its 2nd year with it being on track to sell 20M this fiscal year. So, the best 2 years of the PS4 would beat the best 2 PS3 years by 22%.

Also, what lack of momentum of the PS4 are you talking about here? Because I'd like to know how you came to that conclusion.

And hasn't taken off? It will be outpacing the PS2 again next quarter. How much faster do you want it to sell?

And again - it is on track to sell 20M this year. That's the forecast at least.

Hard to say, depends on the Pro, how the Xbox brand will do in NA for the remainder of the gen, pricing strategy etc. but 100 million should be within reason. With around half that after three years on the market, it would need to sell the same for another three years to get to 100 million fast, factor in a decline unlike the PS3 and 360's unusually late peak due to unique circumstances on the market and ushering of the HD era on consoles and TV and what is likely to be a shorter gen than the last with a steep drop-off once new hardware is made available, and 100 million is a fairly reasonable prediction in my opinion. One could argue that the market hasn't changed that much, the problem with that statement is the relative lack of momentum for the PS4 despite its utter dominance over two main competitors; there should be more room for faster sales according to historical trends, but there doesn't seem to be that much, one console is down and out, or even DOA, and the other is only now selling decent amounts in one major market but slightly flailing globally. The PS4 has, so far, not outsold the PS3's best year by any big margin, which is quite telling given the above factors and the PS3's rather poor start (2015 saw the PS4 sell about 15-17% more than the PS3's best year, the PS3 was a third place console for most of the gen).

In short; with positive press, good pricing, some good software, great functionality and weak competition thus far, the conditions should be more or less optimal for the PS4, yet it hasn't really taken off in the manner that many expected. I still remember how ridiculous many thought I was being when I said that I don't think it will ever have a 20 million selling year. I can still be wrong on most fronts, but so far it seems to be proceeding pretty much as expected.

Some people thinks that this gen will  be very short and that the PS4 won't have enough legs to surpass 100 millions of units.

The PS4 will have atleast 5-6 years of market before the PS5 while the PS3 had 7. The difference isn't that big, the PS3 was the only Playstation console that did not sold 100 millions + units.

We need to wait until after the holidays in order to know how well the PS4 sold. I think that 2017 will be PS4's peak year