I think I love and admire Eydie Gorme just as much as you do. I always enjoyed her appearances on programs hosted by Steve Allen and Johnny Carson because she sang show tunes. As a pop or nightclub singer, absolutely no one ever performed numbers like "If He Walked into My Life" and "What Did I Have That I Don't Have" better on TV talk and variety shows than Gorme. I agree that she was superb, and her renditions were thrilling. Nevertheless, IMO there is nothing that can equal the insight and effectiveness (especially in the context of their stories) that Angela Lansbury and Barbara Harris brought to these same numbers on their respective cast recordings. To me it's like comparing apples to oranges.
I think from the get-go Andrews and Streisand had serious acting ambitions in addition to wanting singing careers. When Gorme was considered for Funny Girl, she apparently told Stark, Styne, and Robbins that her acceptance of the role was contingent on her husband playing Nick. I cannot imagine Julie Andrews saying to Lerner, Loewe, and Moss Hart, "Okay, guys, I'll play Guinevere but only if Tony is the costume and scenic designer for Camelot." Or Streisand telling Stark, Styne, and Robbins, "Sure I'll play Fanny, but only if Elliott is Arnstein." That's the difference I see between Gorme and the two actresses you named.
Just to be clear, I respect your opinions immensely and enjoy reading and (occasionally) responding to your posts.