There's simply no example of this even being remotely likely yet.
I mean people love to use PS Now as an example of this, but really it's just an optional service that allows you to stream older generation titles, certainly no proof that generational, local hardware improvements are being replaced by a broadband/server based approach.
Sony possibly releasing a new version of PS4, with more powerful hardware is just proof that their may be a mid-gen optional update for people, to give them more options for play, though even that will likely just be a tester to see if people like the idea, with the recent backlash of these rumors I wouldn't be so sure it's the guaranteed way forward.
If anything generations may get shorter, but that's about it.
A broadband based platform is inherently unreliable, suffers from latency issues and would be notoriously hard to market from a sales perspective, plus there's the whole inability to really get the most out of such hardware, because it would constantly be a moving target for developers to cater to.
The simple fact that modern consoles have sold better than ever actually points to platform holders not giving that model up, more likely the console model become more prevalent than ever before.
TBH most likely added options will be the way forward, I never understand why people would want something that has worked for so long to disappear.
The best approach is for platform holders to add new features, like keeping the console as the focal point, maybe turn those into personal servers for people to also be able to play their games on the move (whether it's through tablets, phones or dedicated gaming handhelds), then also help to reduce latency through connecting the ecosystem together more and plugging the gaps in latency with added servers that aren't in people's homes.
This kind of stuff takes time to happen too, it won't just be a sudden switch over to this, but rather iteration of added tech into the console ecosystem.
Options people, not lack of options is the future, which means consoles aren't going anywhere for a very long time.