They can keep remaking/remastering games that way! Yay Sony.

Yup, that's all it boils down to. Thanks for bringing up SharePlay, actually. Look at it on paper: you get to share games with your friends for an hour and unlimited amount of times, and they don't even have to own the game. Sounds like a damn good deal....but it's an afterthought for many. It's already been on PS4, and it's "hype" has come and went. BC isn't here yet, so it'll be hyped up. But when it launches for the mainstream audience, it'll be a talking point, then people will forget about it.

Could they do something like basically just sell the PS3 chip in a smaller casing (no need for a HDD/disc drive) and have it connect to the PS4 via a USB 3.0 port ... and voila ... PS3 games? Charge say $100 for it?

Truth is though does Sony even want backwards compatibility? The PS4 is having no trouble selling without it, and by not having it they can remaster those games and sell them again or provide them through their PSNow service, which you will of course have to pay for. I don't see the motivation for Sony to really provide this. 

As much as you oppose it - remasters to PS4 code are actually good for us gamers. Not only are they upping the graphics on the game (and any additional fixes they implement) - they are porting it to x86.

This means two things:
1.) The game is gonna be playable on all forseeable PS consoles
2.) The game will be playable on the x86 version of PS Now when they launch it. x86 servers will be much much much much better for the platform. One of the bonuses about cloud gaming is that they can upgrade their servers (swap out PS3 versions of games with PS4) without the end user having to do anything (as long as they have a DS4 compatible device).

Shareplay is pretty great though. The screen sharing part is fun to show your friends something cool without having to record it.

The actual gameplay sharing is cool to give your friends a chance to try out games like LBP3 that they're too macho to try on their own.

After my playstation3 broke down I had four games I've yet to open so it would be nice for the PlayStation 4 to have backwards compatibility. 

It woulb be great to have BC or PS Now BC on the PS4 but I won't be using it much if they actually do put BC on the PS4.