Well, for one thing, you end up showing interesting things about the history of the relevant part of the world, often things it would be hard or impossible to show any other way – that Madagascar was settled by people from Borneo, for example, or that Ijo slaves from Nigeria ended up on the Berbice River in Guyana, or that Persians and Swedes (along with a lot of other people!) ultimately both got their language from a common source. But that depends on your being interested in a particular region; why would a person working on the historical linguistics of (say) the Sahara care about the historical linguistics of New Guinea, or Alaska, or even Europe?
It’s because people are pretty similar everywhere – we all have roughly the same mouths and the same brains, and as a result we all tend to make roughly the same kinds of changes. Looking at changes in the languages of Europe, and at which direction they went, turns out to give you a pretty good idea of what kind of changes to expect in New Guinea – and vice versa… That means that all these individual small-scale studies are so many pieces fitting together to form a map of how language works.
Of course, as bulbul points out in the comment thread, the real reason is “Because it’s there and it’s fun”!
(While you’re over at the Mountain of Languages, check out Lameen’s latest post, on the idea that in the Arabic-speaking world “Fusha acts to insulate the majority of the population from the debates of intellectuals, keeping the powers that be safer from ideologically-inspired opposition and the intellectuals themselves safer (in the short term!) from popular reactions to their speculations.”)