Ok, I'll bite. I have a laptop in the living room that can, and occassionally still does get plugged into the TV for multimedia use; yet the chromecaste gets several orders of magnitude more use.
Form factor. I don't need or want another box sitting in front of my TV.
Quiteness. I am well aware that a PC can be silent, but it costs money and effort to accomplish. Less so these days with low power micro boards granted.
Power draw. To get into entertainment of choice is significantly faster with the chromecast unless you leave the PC always on.
Phone vs physical keyboard and mouse. Maybe it's just me but I've never liked using a keyboard/mouse on the couch. With a laptop sure, but even a wireless keyboard is a literal balancing act. Even if you have a nice setup with a remote, I can honestly say I know where my phone is more often than I know where the living room remote is.
Portability. The small advantage of being able to take a show with you when you leave the house, I don't use it much, but my kid sure does. If we need to leave they can pull the show at it's exact current point in playback to the phone in a matter of seconds.
Many of those advantages similarly carry over to consoles and smart TVs, but by far the largest is the user interface. Netflix, Hulu, Youtube... they've all put far, far more effort into their mobile offerings than they have their console and smart TV apps and it shows. It is much faster and easier to find and pick a show with your phone than the laggy, disjointed messes that some of those console apps are. Add in the fact that multiple people can be looking for something to watch at once, including across multiple services and it can make a big difference.
Aw crap, all that and I forgot the obvious one.
Price! You can get 4 of these for less than even a cheap HTPC.