The main problem is that AV (and some other Windows software) like to inject DLLs into every single process in the system.
The current trend in browser security is a heavy form of sandboxing, in which the sandboxed processes can only access a very limited set of system calls. For that to work, the set of system calls required by the sandboxed process must be known, which is only possible if all the code running within the sandbox comes from either the browser or the operating system itself.
However, if an arbitrary DLL is injected into the sandboxed process, running arbitrary code and attempting to call arbitrary system calls, the sandboxed process will crash, either because the sandbox mechanism kills the process when it attempts to call an unexpected system call, or because the call attempt returns an error value which the injected DLL didn't expect.
Therefore, browser vendors are unable to enable stronger forms of sandboxing, since they'll lead to crashes in the wild.