It's not about "not trusting the user", but about the user not having to trust the author of the application.

No. Why would it? The user can still grant full access to the machine to applications they trust (like they do now). In fact, the traditional Unix security model (root vs. regular users) was about "not trusting the user" and securing the machine from the user. This "new" kind of sandbox is about the user being able to apply different levels of trust to different applications.

I can see this being useful for running proprietary and non free software. However, we should strive for all software to be free software instead. Because if I download free software, I have the community of developers to vouch for it. If I download proprietary software, I can't really trust it.

My answer to that is "heartbleed". It is irrelevant if you trust the developers - sometimes those developers will make mistakes. Sometimes those mistakes will be serious.

The less privileges your applications run with, the less likely it will be that exploits will affect you.

You think you can trust the authors of every free software package to have kept out all security flaws? That's a mighty happy world you live in.

As a programmer who makes his living selling software I'm not particularly keen on "all software to be free".

Do you run everything as root? Why not, don't you trust the user?