Here are some examples of how well known sites solve the various problems and possibilites of menu systems. This page is not intended as a promption of Taxonomy Treemenu, but to help you to decide how to handle menus on a site.
Wikipedia (www.wikipedia.org) never shows structured lists on information pages, so avoids complex menu and URL customization. This is useful for a site with extensive information, but Drupal's region layout means that that by default, menus will appear on a page. To to follow such a format, a developer would remove menus from sidebars on nodes. Taxonomy Treemenu's role on such a site would be to provide flexible, navigatable index pages. Other sitemap and index modules can offer other display and configuration alternatives.
This site (http://msdn.microsoft.com/en-gb/library/default.aspx) uses a DHTML menu in the left sidebar (on their site, the 'left sidebar' is an HTML frame). The site does not use aliasing, but probably could. This setup is very easy to imitate in Drupal (with aliases also!). You will need a module which can produce a menu from a taxonomy, and the module DHTML Menu.
FThe Ebay site (www.ebay.co.uk / www.ebay.com etc.) uses a hybrid menu system. Each 'node' (auction item) has only one URL, which is desisrable for a large site which may be searched from outside the site context. The site does not use 'treemenus', they use Views type lists, but they could. Ebay never show their lists on the 'node' page, so the developers avoid the problem of how to target a menu within a multiple hierarchy. To help with navigation, the coders provide a multiple breadcrumb, for example,
Your item is listed in, Cars Motorcycles & Vehicles >> Motorcycles and Scooters >> [My FireBlade, may break for spares] Vehicle Parts & Accessories >> Motorcycle Parts and Accessories >> Motorcycle Parts >> [My FireBlade, may break for spares]However, Ebay use customised URLs, as their URLs are huge! The large URLs carry a lot of information, The information contained may be what is needed to construct the breadcrumbs. To finish off this unusual hybrid, EBay inject a human readable name into the middle of the URL!
Drupal with Taxonomy Treemenu can do something like this, by using the 'multiple breadcrumb' feature on a multiple hierarchy taxonomy. You would then use Views, or perhaps treemenus, for navigation, and modify other URLs to follow the treemenu form, thus maintaining only one URL per node.