For me, I want to download and install everything. I want every small thing I do to be its own program, with its own name.
I want to be able to remove my network card and still have programs which work. I want to own everything about my own PC and all the data that enters or leaves it. When everything's in the browser, that's not possible, because you're essentially turning a PC back into a network terminal. I want my computer to be mine. I want my data to be mine. I do not want anyone or any program to have the authority to edit data on my PC over a network without my clear consent. And if you say that installing and/or activating the browser executable means I'm giving consent to it to edit data freely on my machine, then I think I'm going to need to go a different way than the Web.
We need the freedom to have our own computers, our own thoughts, our own data. We need to be able to say at a user level that we wish to interact with this data in our way, rather than "the Web way". Not every piece of data needs to be viewed or manipulated in a way that works in a Web browser. And the processor load should absolutely be a concern. A well-written and optimized program written in asm will always run faster and better when compared to a "program" written in a web-deployed JavaScript on top of a browser.
Why should we be constrained by the lowest common denominator of the Web, when having the ability to use our own offline system enables the use of millions of more user-focused use-cases?