One of the interfaces of web applications, is URL (address bar). It can be considered a counterpart to API (application programming interface) in the same facet that some of the behaviors of the application can be controlled directly from the URL. For example, you may directly type
http://www.yoursite.com/update/john/phone-number-to/9195527768. This way, you can controls your web application directly from address bar and address bar becomes something similar to command line, and URL becomes a command.
Another usage of the URL as others said can be bookmarking. You may remember Back button problem of AJAX applications. It prevented users from being able too bookmark one specific state (or page, or resource) of a website. For example, consider that your site is
http://www.yoursite.com. No matter how much your site's visitor interacts with it, he still sees
http://www.yoursite.com. How the heck he/she is supposed to get a link to one specific resource of your site and send it to his/her friend? Via Firebug?
Also if you don't change the URL while changing the state of your application, no entry would be added to
window.history object, thus if user click Back button, instead of being taken to the previous state of your site (or application), he/she would be taken to the previous domain (maybe google.com, maybe yahoo.com, any domain, but not yours). This is a seriously frustrating experience. Paralle Plesk's control panel works just like what you describe here, and it's awful.
Another usage of URL would be SEO (search engine optimization). Google, Yahoo, and Bing would know and index your site's content based on the URLs you submit to them. One URL, one index, less chance to be found on the net.
I strongly recommend that you redesign your work. No offense, but when we say best practice, we mean something that has been done by many people and organizations. What you want to do is so rare that I can't remember any example of such an application. Best practice comes from repeated implementation of something. I believe that there is no best practice for this architecture.