I have done my research, and yes it is about the way you design your console in the first place. The firmware across the different PS3 models, or even the PS2 models were very much the same. As you say however, you need the hardware for compatibility. Which means you need to include hardware for backwards compatibility, which they're not putting into the PS4 or the Xbone.
As you say, the later PS3 models used software emulation, but this was only in relation to games you bought off of PSN. You couldn't put a disk into your later model PS3 and have it work.
So if they had shipped the Xbone or PS4 with the hardware of the previous gen included then we could play last gen games. But they haven't. And now they're trying to bring out software emulation because they know that they can have us pay twice for the same game. Once for the physical copy, and then second for the software download because they wanted the extra money.
They didn't include the hardware for backwards compatibility because they realised that they'd be able to bring out software emulation, which would restrict what games you could play to games which you bought again