I have never seen Barbra Streisand in a film musical. But, I did not think she lacked warmth or showed "how hard I am working" in either "I Can Get It For You Wholesale" or "Funny Girl." To be fair, both of those musicals were tryouts prior to Broadway.
My parents took me to see "Annie Get Your Gun" with Betty Hutton in Lexington MA when I was six or seven. I did like "White Christmas" and "Pete Kelly's Blues," and perhaps "Easter Parade," but that's it.