That is entirely possible as Sony focuses on making as many PS5 consoles as possible. 

 This is true. The PS4 has had the worst legs in playstation history excluding PSVita, it may not even reach 1.5m for this FY. Sony doesn't care about reaching 120m, i think they just want to be done with the PS4 in terms of hardware, of course they still want to make money from their software with that huge install base.

The key for understand this is: First, aggressive pricing. Sony loses a good profit margin chase install base. It´s happening with PSone, PS2, PS3, but no occurs with PS4. Sony launch a cheap version and lost a good margin with old consoles. PS4 has fews price cuts. Second, PS4 it´s not focusing on a multimedia center, Ps3 and PS2 was the multimedia center focus, so people buy the videogame because, beyond games, it´s a cheaper option and good multimedia center. Sony now focus on profiting ( PS5 beyond June, now making profiting per unit sale) 

And this is what I think Nintendo will do with the Switch. Why sell 15 million Switch 1's to a mostly tapped userbase with dwindling software sales and user engagements when you could sell 17-20 million Switch 2's to a brand new/excited userbase with increasing software sales and user engagements?

The smartest thing for Sony/MS/Nintendo to do is focus less on the generation numbers and more on the annual numbers.

Sony self-destruction ps4 lifetime potential is a strong case study for Nintendo to follow as it no doubt is more profitable for Sony to cut the legs out on PS4 so it can inject steroids into PS5.

You still don't get that selling 15m Switch consoles will result in higher software sales than selling 17-20m Switch 2 consoles. Look at this spreadsheet to get an idea how software sales work.

Switch's highly successful first full fiscal year saw 15.05m hardware units shipped along with 63.51m of software. But when you extrapolate how much software Switch will sell late in its lifecycle in a year where hardware has to declined to 15m, you'll come up with a number that will still be comfortably above 100m, because the existing installed base before that 15m hardware year will still buy software in large numbers. The late stage of a console lifecycle is more profitable than the early stage of it, so if you look at the business with profits in mind, your whole line of thinking is wrong.

Sony didn't launch the PS5 in the year when PS4 hardware sales fell below 15m and it didn't hurt their business that they waited longer. What did hurt them though is that self-destruction of final stage PS4 hardware sales, because it did cost them sales without a doubt. These late adopters may have not bought many games, and not at a high price either, but selling something is still better than selling nothing when it comes to a platform that has been so successful for such a long time. Sony's decision to kill of PS4 hardware sales is also at odds with bringing cross-gen games to the PS4 in 2022; on one hand they want to move people as fast as possible to the PS5, but on the other hand they believe that there will still be millions who want to buy new releases on the PS4 as late as 2022 when it should be clear from previous transitions that software sales significantly break down at that point in time. It's as if they couldn't make up their minds.

It's the wrong premise to look at it as an either-or scenario anyway. The most profitable course of action is to earn the remaining profits from the old hardware while simultaneously building a new profitable platform for the future. That's why Nintendo's transition from the 3DS and Wii U to Switch was handled better than what Sony is doing with the PS4 and PS5. The continued support of the 3DS platform didn't hurt Switch to any noteworthy degree. The Wii U was cut immediately like all failed systems are, because both its hardware and software sales were at such a low level that there was no point in continuing; the market had already sent a clear message that it wants to move on from that disaster of a console.