Lucille Ball as 'Dolly Gallagher Levi'
Given the time period - and the playwright's original vision of the play - AND her full name - Ms. Dolly is presumably a brash Irish-American woman who married a New York Jew. Some stagings and interpretations have the character as more of a Yiddish Yenta, meddling and musing on life in an "oy vey" way, but that ignores the fact that Dolly's maiden name apparently suggests that she is a Gentile,
Obviously in a Broadway musical, liberties can be taken and so an all-black cast of "Hello Dolly!" was/is delightful to watch.
But if you're going to cast the part according what the character most probably looked and acted like, I say you need someone with a brash Irish personality.
I think Lucille Ball would have done interesting things with the part - although she destroyed her voice when she starred in the Broadway musical "Wildcat!" in the early 1960s. (Listen to her in the very last episode of the "Lucy-Desi Comedy Hour" and she still has a bell-like toned voice; compare that to her gravelly voice that came to distinguish her later "Lucy" characters in "The Lucy Show" and "Here's Lucy").
But she could have danced very well and when Dolly reminisces about her popularity in the past, Ball's reputation would have made those memories seem all the more vivid to the audience - not to mention that when Horace Vandergelder calls Dolly a "damned exasperating woman" it would seem entirely appropriate AND humorous to the audience.
At any rate, I think Lucille Ball could have done an excellent job as Dolly in the play "The Matchmaker"/"The Merchant of Yonkers" by Thornton Wilder. She wouldn't have had to sing, that's for sure.
"Don't call me 'honey', mac."
"Don't call me 'mac'... HONEY!"