Here's a popular musical number from a remake (2003)
Here's the original:
The more modern version is racially integrated. It also has only pretty people.
There are plenty of pretty people in the 1962 version, but there are also what my wife calls 'faces'. That is to say non-pretty people with distinctive looks. In the modern version the mayor and his wife are youthful and very pretty. They are portrayed by Victor Garber and Molly Shannon, both of whom are quite good looking.
In the 1962 version, the mayor and his wife are played by Paul Ford and Hermione Gingold, neither of whom could be described as beautiful. What they did have were faces with character, distinctive voices (hearing Hermione Gingold say 'Balzac' is worth the price of admission) and serious comedic and acting chops.
Somewhere in the forty years between 1962 and 2003 Hollywood lost track of what character actors should bring to a movie and started casting pretty people exclusively.