Indeed, you are correct.
However we seem to have a bit of a sticking point when it comes to power of devices.
I guess I'm speaking more of dumb clients, so the mobile device would pretty much just be a screen/input device with almost no power, and your home box? could do the rest of it, and act as a middle man to the cloud.
Even with chromebooks now, we're looking and higher and higher power versions coming to get their speed up.
And of course Tablets/phones are getting more powerful all the time.
How about when you got home this all stopped and your home box? took all this work over so they'd all last for a week? as they were doing almost no work?
Just a thought
I'm sure in most old sci-fi films this was the idea.
One central machine and small devices which communicated with it.
Not all carrying around independently powerful devices.
New games console?
Nope, as it runs from your main home box
Perhaps that's one of the biggest reasons? there is just more money to be made selling us newer/faster individual devices each year