The general concept of curl only doing the bare minimum unless you tell it differently makes it not acknowledge cookies by default. You need to switch on the cookie engine to make curl keep track of cookies it receives and then subsequently send them out on requests that have matching cookies.
You enable the cookie engine by asking curl to read or write cookies. If you tell curl to read cookies from blank named file, you only switch on the engine but start off with an empty internal cookie store:
curl -b "" http://example.com
Just switching on the cookie engine, getting a single resource and then quitting would be pointless as curl would have no chance to actually send any cookies it received. Assuming the site in this example would set cookies and then do a redirect we would do:
curl -L -b "" http://example.com