It's incredibly hard to say since we can really only speculate, but I don't think it has anything to do with how much they "care", it's all about money. I'm sure backwards compatibility would sell the system for a lot of people, so I'm sure that they've at least considered it, but concluded that with the new hardware, it just won't pay off to add the backwards compatibility in the long run. Yeah, I'm sure the selling of PS2 (and in this case, PS3) classics had an influence on the decision, but I highly doubt Sony gathered their smartest crew to come up with the most villainous way to screw over their consumer. As for the Vita having a dedicated memory thingamajig, I completely agree on that, I fucking hate those specially designed Sony memory cards and I think it was a stupid decision to go that route. Definitely killed the system for me until it gets a price drop.
As for Nintendo and their use of backwards compatiblity, I must once again refer to just how little I know about the economic and technical side of this. I'm sure someone with better knowledge of console hardware than me could come up with a point for this discussion, though.