What is really the purpose of streaming??

Its mostly about easy access to music.  It can also be about top notch sound but does not have to be.  Same true about records, CDs, whatever.

CD or streaming can both be top notch if done well/right.  Same true with vinyl.    

It is probably easier these days for most people to have a chance at getting top notch sound at an affordable price using streaming.    Also streaming offers many user experience focused features that many will find beneficial in addition to the sound quality.   Of course some will not...

So combine cost, good sound quality and a myriad of value added features available and its easy to see why this is where things are and will continue to go.

I think it is mostly about convenience, but if you use Roon with Tidal it can show you music that you can discover, like, and possibly would have never thought to hear.

There are no sonic differences between cd's and red book 16/44 streams as from Tidal or Qobuz (provided the same DAC is used, of course). The difference is the convenience and the access. The latter in particular is something I value greatly. Suddenly you have access to a very large proportion of all music ever recorded.

Streaming allows you to access more music than you could ever possibly own.  If set up properly, sound quality is not an issue.  There are issues regarding how people can sort through and digest extremely large collections.  Most algorithms are based on "if someone listened to X artist, what else did they listen to".  Most people find that very helpful, but some don't.

Not all "streaming" works the same way.  Spotify (various resolutions, not yet high res, sometimes CD quality) and Tidal (higher resolution, usually CD quality or better, more limited catalog) are subscription "streaming" services.  They do not use physical CDs, of course.

Then there are local hard drive devices (network attached storage) for music storage.  Music files from NAS devices can be played using "streaming" hardware ("streamers").  Again, no physical CD media, but the files are stored locally on the NAS or similar devices.  

The latter approach is the one I use currently, and it allows one to avoid keeping track of physical media (CDs) while accessing all of the stored CD albums via tablet or phone touchscreen app.  VERY convenient, and in my system sounds at least as good as a CD player (i.e., physical media player).