If you spend 380 million in a company that it is based in Cloud gaming you don´t need to be Einstein to see it (possibly) included in the next-gen console.
Even if they use it only for *solving* of the backward compatibility problem - as theory suggests it will be the main purpose in the first phase - they've still went with good price.
380 million$ is 10$ cost per-console once they've manage to sell 38 million PS4 consoles. From that point onwards they have paid-off the investment. And we can all agree how hardware-driven PS3 compatibility (we can presume the PS1 and PS2 games could be emulated by PS4 hardware, it still remains will they allow it, but that is not an issue now) would cost more than 10$ per console.
So it is a good investment, especially if it allows for instant PS4/Vita cross-play, streaming of demos, pay-per-play model for *Suite* titles, etc.
Also, I presume how streaming (pay-per-play) for PS4 titles will absolutely be an option. At this point Gaikai is investing gained funds into development of 1080p/60fps GEFORCE Grid infrastructure (they've currently reached 720p/60fps, with 1080p as final goal of the upgrade).
And PS4 (X720) games will render from 720-1080p@30-60fps. Despite new technology and stronger hardware I think how 1080p/60fps games will still be rare. Majority of the next-gen engines will be used by developers to target locked 30fps with resources being spent in area of real-time effects, particles and such. Focus groups and general audience does not prefer 60fps fidelity over attractiveness of effect-driven 30fps with strong emphasis on more *wow* factor. So 1080p/60fps will still not prevail on the next-gen.
4K resolutions will probably be possible with PS4, but I doubt how 4K games will become reality (with exceptions of few that *could* offer the option as some kind of demo or special mode, as GT probably will - Polyphony demonstrated 4K GT5

rologue back in 2008). 4K resolution will be integral part of the Blu-Ray output, while 4K games will probably arrive in the next-next gen, around year 2020.