"I certainly do disagree. Bear in mind that Beatrice Arthur starred in sitcoms. Very intelligent sitcoms, to be sure, but sitcoms allow for and often require a broad quality that might be right at home on certain stages but would not work at all on film or even in subtler and more dramatic television shows."
I think that's a huge generalization. What you say is very true in some cases and absolutely not true in others -- it all depends on the property. Also, I think you are using precisely the wrong word when you label Beatrice Arthur's acting style in MAME (or in anything else) as "broad." Quite to the contrary I would describe her style of comedy as very subtle for the most part, and often what might even be described as deadpan. Again, it's the costuming and makeup of her character in MAME that are so campy and over the top, not her acting.
To make this discussion even more interesting, I would say the non-musical film of AUNTIE MAME has some of the broadest acting I've ever seen in in any movie, and some of the production and costume design in that one are quite over the top, as well. I would describe the film of the musical as quite a bit more restrained for the most part, with Arthur's costume design and makeup as an exception. The way she was costumed and made up in that movie, her performance would probably have fit better in AUNTIE MAME than in MAME.