You gain the protection from a man-in-the-middle attack where a 3rd party was sniffing traffic and was able to replicate your login from their system by copying your cookie. By encrypting the cookie with the IP of the client connection, the would-be hacker would have to hack his connection to make it look like the TCP connection from his system was the same as yours which is very difficult to do. You are correct that this would work on any other browser on your current system but typically if a hacker has gained access to your operating system, you have more to worry about...
-Joe
