The configuration you’re describing is totally viable, and is in fact quite similar to something we considered for our nginx implementation on DreamHost VPS. The problem, as always, is in the details.
See, Apache gives users a lot of flexibility in how they can configure their sites. mod_rewrite, directory aliases, and a number of other Apache features can all conspire to make it very difficult, or even impossible, for a front-end server like nginx to figure out where to serve files from. Worse, such a configuration could potentially end up bypassing security measures set up in .htaccess files, like password protection, IP blocks, or “Deny from all”.
For a carefully architected application designed with this architecture in mind, a reverse proxy setup like this would be no problem. Experience, however, has taught us that some of our customers’ applications are often… less than that.
In any case, the performance advantages of nginx are generally not relevant to sites running on shared hosting. If your site is busy enough that you feel that Apache is holding you back, your site should probably be on a VPS or dedicated server.