First of all, Mame was hardly a Broadway classic to begin with. It's run was "forced" by the constant changing of leading ladies (Janis Paige, Ann Miller, etc.) to continue interest in show similar to what Merrick did with HELLO, DOLLY!
Title song is a ripoff of "Hello, Dolly". Pure and simple.
In order to play Mame, one must 1) be able to sing; 2) act comedy and drama and 3) support other cast members in their "big moments." [Like Gooch's Song.]
Lucille Ball 1) cannot sing; 2) does situation comedy; and 3) hams every scene she's in.
Lucy as MAME? That makes about as much sense as a remake of THE WIZARD OF OZ with Britney as Dorothy.
Trivial Pursuit: The original choice for Broadway Mame was Judy Garland, but management soon got concerned regarding her reliability issues.
"I say YOU'RE the CUTEST one. No, I say YOU'RE the CUTEST One. And we go on like that from dawn to three."