In general, you want URLs that are short, clear, memorable, and stable. You want to tell people, "Come to mydomain.com/blog," not, "Come to http://www.wordpress.mydomain.com/stamp_collectors_heaven_bl... The latter includes lots of information that their browser + your server can figure out, so you shouldn't be burdening your (potential) users with it.

So, regarding the "index.html" portion: The index is the default. There's no point having a default if you have to specify it, and there's no point specifying it if it's the default.