How do Chromecast, Miracast, "Ipad cast" work? I suppose the wifi hardware can multitask (think MIMO, 802.11n) and it may be why casting things tend to use a special ad hoc wifi link between the two things.
It's doable, more so with 5GHz wifi but 60GHz wifi is better suited to displays. Given that 60GHz wifi isn't available yet, doing this wireless is a big waste of spectrum and power, I agree with that.
I supsect someone will make a wireless laptop shell after this one gets wildly successful, but it would be more expensive too, requiring a real ARM SoC inside and thus making the shell.. a laptop.
What the shell is using is not Chromecast protocol though, everyone gets that wrong. It's Displaylink. What does that mean is it's a USB 3.0 to display adapter, same as you can buy for your PC.
It's not the greatest thing but reportedly, it got much better compared to early USB 2.0 adapters : usable video playback is achievable ; early ones were mostly for documents and powerpoints etc. (e.g. interface to the corporate projector if you lack other means)
I'm sure that made the design much easier : you merely have to bundle a Displaylink chip, a USB hub and glue them together with the display panel and keyboard etc. and you don't rely on the phone supporting display output (various). The Displaylink and panel (LED lit) became very low power compared to a decade ago.
If the phone does only USB 2.0 it might be slow (I know nothing of USB 3.0 software and hardware support on phones) but will do command line terminals and word processors fine.