By web application, I presume you mean for example google docs, rather than a browser.
This would make it even less consistent, wouldn't it? Some pages/apps wouldn't have these controls, or they would look different or be in different locations across different pages/apps.
"Back" and "Up" are virtually indistinguishable for an average user. Hell, I'd be surprised if I could give a good description about the difference, and I know computers inside-out.
> There is absolutely nothing preventing web applications from giving a superior navigation experience than a one-size-fits-all web browser buttons.
Except for the users...