As compared to the Xbox One?

When did the XB1 add BC? I guess we could check from there and see if sales have gone up since then (although there are obviously other factors too, so as I said before without knowing the what-if scenario it's impossible to tell its true affect).

Wouldn't it make more sense to see if it affected the XB1?

I don't think I ever claimed that the PS4 needed backwards compatibility to succeed, it would make the console better overall though.

Necessary in what way? Obviously I don't think it's necessary as the PS4 functions without it, but I do think the PS4 would be better with it.

Every single R&D cost money and they will have to get it back, it will be charged  in products... and the way you asked on the OP it is more like PS4 should have been developed with BC in mind. So that cost of R&D and manufacturing would be part of the cost of the console that everyone who buys, wanting BC or not would have to pay.

All of that is pretty, still on console field so far BC have been more like a token than of significance... sure enough that I don't even consider BC on PC since PCs are BC and FC for decades depending on your build.

From what we know X1 on the months after release of BC had an average of 5m per user who used BC on it.

Sure for me I would like PS4 to have BC on all gens before and wouldn't mind paying the extra cost, but I understand the lack of market interest and that Sony would lose more than win with it.

He isn't forced to buy a console for sure, but if you just have the PS4 with BC, then the cost to make BC is charged on it and he can't avoid it and buy a PS4 without it (as going by the discussion premises).

A lot of people were bothered with the extra cost of the kinect they didn't want and you saw what that brought to MS. We also know that PS2 BC on PS3 costed them between 50-100 on the console and it was another point to make it a harder sale on the start of gen.

The PS4 CPU isn't much more powerful than a Cell CPU not enough to emulate it. My PC argument was to prove my point. There is lots of interest in PS3 emulation and huge support for it but its a difficult job. Sony can't make the PS4 hardware do wonders there are physical limits to what the PS4 can do.

They don't have a magic wand to make PS4 powerful enough to emulate a PS3. I doubt you understand just how weak the Jaguar CPU on the PS4 is and the difficulty of emulating a very different architecture on hardware that's not vastly superior to the hardware you want to emulate.

It would be possible on the PS5 if it has a Zen CPU there's no doubt about that. PS4 just no.

The PS4 is more powerful than a PS3, the argument that since PCs can't run it does sound fine, but even original Xbox games don't have solid emulators on the PC, despite the fact that the 360 had some BC support and the Xbox One does too:

From what we know X1 on the months after release of BC had an average of 5m per user who used BC on it.

True. Fair point. But the PS3 and PS2  were very different architectures, so it took much more to implement it. Now, with PS5 most likely going to have X86 architecture with AMD based cpu/gpu (just like the PS4), that cost will likely be well below 50 bucks. Think of how Wii had gamecube BC while only being $249. Or XBO, PS2, GBA, early DS, 3DS, etc.

It cost money to develop and make the BC on the console, the customers are the ones that are going to pay for it one way or another.

The 5m is a reference to 5 minutes, not 5M as 5 Millior users. So BC was so relevant to the X1 players that they didn't even play much when they got it.