This is a great question. Style in linguistic is important for many reason. Let me list a few of them.
First, style in linguistics seeks to explain why an individual or group chooses a particular use of language. The assumption is that there are many options in language. By studying this aspect of linguistics, scholars can gain many insights about worldviews, social class, and other interesting information.
Second, style in linguistics also encompasses the studying of regional accents, dialects, and other finer points of grammar (and general language use). All of these details can be used to gain insights. For example, by studying accents, a scholar may be able to study group relations. By studying finer points of word usage, a scholar can trace the etymology and development of a word.