BC for the PS4 would be a nice thing for it to have, especially new owners, as they can play games they missed on the PS3, but I don't think it would have a large boost in sales. People are buying new consoles for new games, and not to play old games. It'd be a nice plus though.

Hypothetically speaking, if people did like mentioned in the OP and PS3 owners started selling their console on a large scale, the value of used PS3 would come crashing down in few weeks. After the value went down, people would stop selling their PS3. It cannot work like it is mentioned in the OP.

I think it would be more like that: PlayStation Four backward compatibility would save "PlayStation gamers" a lot of money...
Sony is not interested at all with this perspective...

Not happening...

This is such a fallacy...

In terms of remasters, there aren't  as many as you think. 
The people that buy these remasters aren't usually people that played the game recently -- or already own it for the very last gen console.
If they do buy it again -- its because of some major enhancement (see Diablo 3... its not an actual remaster but essentially a remake of the entire game that they relaunched on both consoles simultaneously -- yet abandoned support of the old gen consoles).

By offering previous generation games on the PSN store, they actually continue to gain revenue from legacy games. Final Fantasy VII often sold for $10 -- of which sony probably got between $3-5. This is a game that I actually own on disc, but would repurchase digitally just to ditch the stupid PS1 disk.

You WILL see PS1/PS2 backwards compatability. PS3 just isn't feasible -- if it was, Sony would make way more money from offering those old games digitally on PSN than from not.

The PS3 runs an ENTIRELY different architecture and language than the PS4. To emulate it you would need an extremely powerful PC (Which the PS4 is not) and a ton of time. 

This is very true, it will never be an issue again on Xbox and Playstation as they are more than likely never going to move away from x86 architecture. 

Also about the PS3 emulation thing according to Ubisoft the PS3 CPU is actually more powerful than the PS4 CPU.... So yeah.... It is not happening (this is not directed at you)

http://media.redgamingtech.com/rgt-website/2014/10/ubisoft-cloth-simulation-ps4-vs-ps3.jpg

The cell is not necessarily "more powerful" than the PS4 CPU. The clock speed of the Cell is higher than the jaguar -- the jaguar makes up for this with significantly better parallel processing, and newer tech.

Trying to brute force a slower CPU to emulate a faster CPU is ASKING for trouble. While you could hack things to use parallelization to handle this -- it will cause threading nightmares by having things processed out of order (for example thread A is expecting the result of thread B -- but thread B gets its IO task completed first and doesn't have the most currently value of the output variable of A).

I'm sure PSnow can make a lot of money too. And be much more important in the future than PS4 backward compatibility. Which is probably impossible because cell and stuff.

"Such a fallacy"... Really... please :)

Sony (like any business) is going to go for the most profitable. And with their service (PS Now) + the success of the PlayStation Four there is just no valid reason for them to do that. People could play their "existing" PlayStation Three digital or disk games without buying new ones or paying for PlayStation Now. This would save money for gamers... yes... How can you argue with that lol? Like remasters are the only games people would buy... You are not representing the majority when you say that you would re-buy all your disk game digitally, the majority will just put their disk in the console and play it... (saving money in the process).... And I'm not even counting all the digital games gamers already own.

Same goes with Xbox One BC... I'm using all of my "existing" games (digital or not) and I do not need to buy them at all (remaster or not). At the end, it saved me a lot of money for sure. (I'm on the preview so I can already play almost all my digital games)

In brute power the cell is the more powerful CPU. But as you were saying that does not make it a better cpu. But the PS4 CPU emulating the PS3 cpu can not happen, the PS4 CPU would need to be much more powerful than it is to achieve that