The sentence before "being smaller than previous popular styles" says they "allowed stylish gentlemen to show off the most current fashions of their wigs". History of Men's Costume by Marion Sichel essentially said the same thing.

Another thing is if you put the development of fashion in a timeline you can usually observe how they evolve by slightly altering what's fashionable previously. Here's how tricornes are smaller than previous hats and happens to coincide with hairstyles: In the late 1500's both men and women wore hats with a smaller flat brim and a tall crown we often think of the Puritans wore, they are called capotain. In the early 1600's capotains grew shorter and the brim grew wider, the brim is slightly curved. Around the same time people who are more adventurous would wear even more upturned brim hats. During the mid 1600's hats grew more and more elaborate with feather and ribbon trims, and with one side of the brim pinned up instead of just curled up. As you can see hair at this time became longer and curlier. By late 1600's and early 1700's hats became full tricorne, but the style actually caught on a few years later when curls were placed on side of the head instead of hanging long and loose.