No, it shouldn't, and Kaz himself basically said so right before the PS3 launched. The PS4 should be HARDWARE BC with all former PS consoles as it's basically pennies on the dollar to make the PS1 and PS2 chips. The Cell would cost a tad more, but again, it's now 7 year old tech.

I'd pay $600.00 again for full BC and I know alot of hardcore gamers would as well.

I think this is the best way to go about it too, I'm the same.

In fact I plan to bring my PS2 to my main TV when I finish all my PS3/360/Wii games (or at least most of them) to start up some great PS1/PS2 JRPG's. Drakengard 2, Suikoden, XenoGears and Grandia all rank high in my TDL.

go get an older model ps3

Lower Price or BC? Which is more you important to you? But more importantly, which is more important to the gaming market at large?

Lower price beats a feature that few people would care about. It may seem simple for PS4 to play PS3 games, they both use blu-ray after all, right? But the PS3 is so vastly different than other consoles, while the PS4 is a more standard design. It would take a lot of work to get the PS4 to properly emulate a PS3, and it might not even be possible with their different hardware designs.

nobody buys a new system to play old games, yes the feature would have been nice, but it's far from being make or break

What matters is transitioning to new platform from older version.  I understand possible need to drop it, but lack of backwards compatibility means a lack of a hook  for owners of prior generation to migrate up.  People will stall and wait for things to pan out and milk the content of current generation. 

Gaikai BC will probably be on Plus or some subscription model.

Meaning BC will not be a mandatory thing for gamers to buy, like it was on the PS3, which made you partially buy a PS2. In that respect I actually much prefer cloud gaming when it comes to old games.

The logic of this argument astounds me.