I've never understood why a weighted WoT system has never become popular. I trust some friends implicitly, and I trust some other friends less. I trust friends of friends, but generally less than I trust direct friends. I'm still willing to trust someone who two friends friends know, and if you can trace me a dozen lines to Kevin Bacon, I'll trust him, too. Sure, there's some hard graph theory and weighting to be done, but I can't imagine those aren't problems that can be solved with modern big-data techniques.
If someone sends you an email and you partially trust the key, how does that map to the contents of the email? How does it map to executable code? Source code? Images? Digital signatures?
It's like saying some people's trust is a square circle. It's a correct sentence but it doesn't map to any meaning usefully.
As two examples: Partial trust means you trust a key for different purposes, or for different levels of validity.
Different purposes: "Do I trust that this key correctly identifies this person?" is a separate question from "Do I trust this person to do proper verification before signing others' keys?" (i.e., trusted link in the Web of Trust)
Different validity: "I've met this person and verified they own the key", is different from, "They've identified themselves with two forms of government ID", is different from "I've known them all my life".