Why are web browser programs computer based software and not Internet based?

Computers require instructions (which programs and software basically are) from somewhere. Usually the location of most convenience is in local storage, which is the closest.

In order for a program to be Web-based, it has to be hosted on a server somewhere else. The idea of having a Web browser hosted somewhere would make the purpose redundant (as in defeating the purpose since you'd have to get on the internet to browse the Internet).