I always assumed (probably incorrectly so) that the reason longitude and latitude are handled in DMS is simply because longitude and latitude represent positions of angular displacement, and what other natural form for handling angles exists?

IE when TD#5 (here we go again, eh?) is listed as being at 10.8N and 42.9W, it's saying that the storm is parked 10.8 degrees above the equator and 42.9 degrees west of the prime meridian.

Now, it would be equally valid to say that TD#5 was located at 0.188 radians N and 0.749 radians W. But, unless you are a math nerd like me, you could care less about radians.

For what it's worth, I found the following link to be wonderfully handy in finding distances between 2 pairs of long/lat, as well as educational overall:

Great Circle Calculuations