Why do shared photo streams take up space on my iphone?

From my understanding shared photo streams were part of cloud storage and essentially you can upload an unlimited amount of photos.
But after I created several albums and invited my friends to share their photos to the albums my phone's storage filled up in minuets.

This has really dissapointed me becuase I love the design of shared photo streams. They are a great way create group alums with my friends.

Are there any alternative services that would allow me to create group albums with friends WITHOUT killing all of the storage space on my phone?