The adjective “handsome” actually has meanings other than just a pleasing or impressive appearance. It can also denote something marked by a moderately large size, as in “a handsome offer”; or something marked by generosity of graciousness, as in “a handsome gratuity.” In all these denotations of “handsome,” we use the comparative “handsomer” to indicate who or which between two entities has the stronger attribute of “handsomeness,” as in “The talent scout thought that Talent A was handsomer than Talent B” and “We got a handsomer offer for our beach property from the foreign buyer than from the local one.” On the other hand, we use the superlative “handsomest” to indicate who or which among three or more entities has the strongest attribute of “handsomeness,” as in “The talent scout thought that Talent A was the handsomest among his stable of 12 acting talents” and “We got the handsomest offer for our beach property from the American buyer than from the Chinese, French, Japanese, and Australian buyers.”
I’m not sure if, as you say, “handsomer” and “handsomest” are seldom used in the Philippines. If you mix with the advertising agency, modeling agency, fashion agency, or movie industry crowd, I’m sure you’ll hear that comparative and superlative being used uncountable times 24/7—no matter what the American Heritage Dictionary of the English Language has decreed about the usage of these two adjectives.