Really too bad none of these cause a notifcation. The major reason many use Spotify is the social aspect.. and Spotify dropped the ball on this one. Spotify is the best music platform hands down, and it's really dissapointing they haven't pushed the social scene better (the side bar is genius.. we just need more!).
TLDR: Having more notifications as well as more social tools (like a posted news feed) would really improve the platform.
Updated on 2018-06-16
As mentioned, a similar idea has already been suggested here:
It has been discussed within the Spotify Team in charge and it has sadly been decided that this idea will not be implemented any time soon. However, Spotify will revisit those idea topics from time to time, so hopefully it will be implemented in the future. ;)