So maybe there should be one "left-hand" navigational structure, and an alternative structure for how the site map is laid out?
Yes, there can (and should) be several concurrent or alternative navigation structures, but not too many of them. You have to think through carefully what they're for, and be careful that they don't detract from each other.
And I wouldn't make the human site map my home page, unless it's a very small site. Optimizing a very large site, IMO, is all about data organization and prioritization.
For purposes of discussion, I'm sloppily going to use "PageRank" interchangeably with link juice, link equity, link love, etc.
Thinking just about top-down nav structure for a moment... you want to distribute your homepage link juice wisely, which means that you don't want to give any page a much larger share of link juice than it needs, nor do you want to give it a much smaller share than it needs. While you also have lower level category pages as inbound link destinations, it's helpful to start with a logical home page structure....
In the example that had been posted previously in this thread (which got lost in the server migration)... there was a suggestion that all products be funneled through one "Products" link from home. I don't think that was a wise idea... it's much too narrow.
What the poster suggested as his second level pages... main product categories... were in fact a much better set of links for home. You need to organize your products into main categories and then subcategories, and to link to those main categories from home.
What often happens, though, is that there's a huge temptation to link to your subcategories from home as well. Some product sites also link to individual products from home. Some of this can be done for emphasis, but the more links you have on your home page, the smaller is the share of PageRank-associated link equity that is distributed by each link to the pages below.
So the more subcategories you link to from home, the less link juice each of your main categories gets... and very quickly, unless you're very careful, you put yourself into a position where, if you link to very many subcategories from home, you've almost got to link to all of them. This, IMO, simply doesn't scale very well in terms of semantic or structural clarity, and it fights usability.
Just as a user might have a hard time picking out the right link from several hundred on a page, so might Google. A hierarchical structure with a well thought out taxonomy, with deep links only to your most important pages, is a much more strategic way to go.
The home page of dmoz.org [dmoz.org
...] is a page I've pointed to over the years as a good example of a page where deep links to popular subcategories work well for users and for search engines.
IMO, small sites can't link to as many subcategories from home as megasites do because they don't have the link juice to support that much navigation.
I frankly don't want to get into much greater detail about what I do, because we've all got our secret sauces. But I see that there's a lot of stuff being pushed around the web about having very "flat" sites to preserve PageRank between levels, and I think that the link equity lost in the drop between levels is insignificant compared to the semantic confusion that many sites have with a hundred or more nav links on a page.