Sometimes you want to do something that curl cannot express, e.g. timing, protocol oddities, etc. For example you may want to issue a CONNECT to an echo server through a proxy and observe the bytes flowing back and forth. You may want to see what happens when conflicting hop-by-hop headers are specified without worrying about the client's (curl's) interpretation of them. A simple nc -c (or openssl s_client -crlf) lets you do all of that.

Because curl is not installed in minimal docker images.

because in those days there was no curl, or wget. and then when there was, there was no guarantee they'd be installed.

telnet was always there though. it also worked for speaking all the other plaintext internet protocols. (imap, pop, smtp, etc)