Why do we use the singular in a comparative sentence?
The "any other" construction takes the singular because the comparison is one-to-one.
She is more beautiful than any other girl.
is equivalent to:
She is more beautiful than any other individual girl.
You could express a similar sentiment with a construction that takes the plural "girls" like so:
She is more beautiful than other girls.
But this works because, in this case, the comparison is one-to-many.
In short: as an adjective in this case, 'any' can take the singular