There are a few problems with that approach.
A: The package on the site is only updated for major releases (0.5.6, 0.5.7), not minor releases such as 0.5.6.1. I wasn't able to update to 0.5.6.1 (ever) because the updater on my client broke and it wasn't posted on the site. It wasn't until after 0.5.7 was released that I found and fixed the problem with my client.
B: I'm not entirely sure of the implementation details of the updater, but it most likely saves bandwidth to use the built-in updater. I would expect that the updater only updates things that are out of date, and ignores effect files, etc. that haven't changed. Assuming this is true, then the updater uses less bandwidth than re-downloading the entire client.
C: It's less of a hassle to use the updater (when it actually works!).