The home client is about simplicity
We may have many devices in our homes but they can't require the same degree of "care and feeding" as traditional PCs.
I continue to think that device, a relic of a time when electronics cost relatively more than they do today. That's not to say it never happens. Today, smartphones often function as MP3 players as well and game consoles increasingly are a portal to many types of digital entertainment, not just games. That said, the general trend seems to be toward more consoles, displays, PCs, pads, and mobile devices rather than fewer.
There's an important point to consider though. Reader cvaldes1831 sums it up nicely:
There is one very practical reason to limit the number of computers in the house: system administration time. Even for something that requires very little sysadmin effort (like my three-year-old MacBook), the minutes and hours add up.
I could afford several computers, but I simply don't want to administer more than one system (I'm single).
This is my experience as well. I have a laptop that I use as essentially my downstairs browser when watching TV or wanting to pull up a recipe while cooking. But if I haven't used it for a week, it invariably wants to install updates for Windows, Firefox, Java, or some other system component or program. It also doesn't necessarily start up right away. I put up with the nuisance in this case, but the "care and feeding" of a computer running a general-purpose operating system definitely limits how many such devices I have around the house.
Thus, "more devices" needs an asterisk. And that asterisk notes that updates must generally be automatic and unobtrusive, that new components or applications can't require complex installation, and that the device in question just works doing whatever it's supposed to do. Relative simplicity vs. complexity and single-function vs. multi-function will vary by the task at hand, but the common thread is that all will need to be much simpler than the PC of today.
These home devices may be computers, even vastly powerful ones by historical standards, but they can't appear as such.