Why do historical linguistics?

Unraveling the details of a given language family's history is painstaking, detail-oriented work - comparing hundreds or thousands of words to each other, looking through different languages' grammars, coming up with hypotheses to explain what you see and hoping the next language you look at doesn't disprove them... Why do it?

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; wherever you go, k is much more likely to change to g than to n, and a word meaning "want" is much more likely to become a future tense marker than a word meaning "jump".

That means that all these individual small-scale studies are so many pieces fitting together to form a map of how language works. Describing a language (no mean challenge in itself) shows you one set of possibilities; typology tells you the possible states of a language; but historical linguistics relates them to one another, showing you which states are closely linked and which are not. You can't predict what will happen to a language, but you can see in advance what kind of changes are likely and what kind are unlikely.

For sounds, this map of changes - this network linking different states of a language to one another - will seem familiar; it corresponds closely to articulatory and/or auditory similarity. You can mostly account for it by knowing how different sounds are made (with the lips, the tongue, etc...) and which sounds are hardest to distinguish. The key test for a theory of syntax (as far as I'm concerned) is whether it can account similarly for the attested map of syntactic change.