Right, and it would be far quicker to add content to a handful of pages than to redesign the site structure, not to mention redesigning the home page. Also, I'd need to 301 those second-tier pages, which could hurt -- at least for a while. On the other hand, I've always been concerned that my link structure goes so deep to get to what most readers really want to access that it's a turn-off. It's a logical structure, and it made sense in 1996 (when I first designed and put of the site -- yes, you read that right: 1996). But a navigational structure that mimics a book's table of contents just isn't what users expect or want anymore from a site that is not clearly a "directory" or an academic work.
But I'd still like to know whether, all else equal, a deeper link will rank lower than one that's higher up in a site's link structure. My understanding is that the GA analyzes your taxonomy and assumes that your intention is for pages further up the tree to be assigned more importance that ones further down. If so, that would argue for a flatter directory structure where the real meat (as opposed to the thinner, second-tier) is currently a bit too deep.