User DennisAleynikov in this thread says he has it working with a $20 USB-C to HDMI cable, without even needing to buy the official Samsung DeX connector. Once plugged in, the phone lets you run desktop Android apps straight away.
Check the Samsung DeX page to see how it looks. The use case you've described is already here.
Cool. Still, availability, word of mouth, marketing, etc.
It's one thing when a random person (no offense, Dennis Aleynikov) does it, another one when you have 6 big companies competing for this segment.
And I'm not sure the software part is here. At least not in a polished way. The closest solutions that come to mind are Microsoft UWP (but Microsoft doesn't seem to be gaining traction due to various reasons, not least because they're Microsoft and few people trust them these days...) and Ubuntu Unity (I think they've abandoned the concept?). From what I've read Android tablet and desktop apps are not really up-to-par, at least today.
It should be trivial for me to turn my phone into a computer. I should need only a $20 USB hub in order to power my phone and connect it to a keyboard, mouse, one or even several screens. Or even connect them wirelessly.
Then, the OS should trivially handle this case and offer me access to high quality desktop apps.
I don't think either condition is true now.
When this point is reached I'm pretty sure half of the laptop sales will evaporate within a short time.