I was under the impression that PS4 hardware basically just needs to bridge the gap until Gaikai takes off, i.e. fast internet connections become widespread enough to make any new home-console hardware revisions (generally) unnecessary.
SONY's next "console" hardware will probably just be a Vita-TV-ish Gaikai streaming device that's capable of 4K output. Which is to say: As soon as they get Gaikai going, they won't only be able to take care of backwards compatibility on PS4 by adding some of the more beloved PS3 games to their Gaikai catalogue, they will also be capable of "launching" a new "console" by building a few new server farms, running their games with "next-gen" specs on them and putting them behind a "PS5" Gaikai paywall that can be accessed/streamed through local PS4 hardware.
So, yeah. Don't be surprised if PS5 basically just ends up being a "virtual"/"software" console realized via Gaikai and centralized servers, accessible via PS4 or any other future Gaikai-enabled device.
In that case, PS4's lifespan will basically last until the machines take over.
As for XBOX One, I really think their current cloud-computing approach is very interesting, but also very limited in real-world gaming usability. So they either come up with some better hardware in 5-7 years, or implement straightforward, Gaikai-type game streaming.
All that being said, there'll, of course,
always be a certain market for fast "offline" console hardware - but I really think that this market will shrink significantly during the next 5-10 years - probably to an extent where a statement like "we do have an offline console, it's called PS4" won't make any huge splash anymore and powerful local console hardware becomes a niche market taken care of by really fast (and expensive) "Steam Machines" that have shorter life cycles than iPhones