The issue with C is not the language itself. It's the complexity of the project. Once a project reaches a certain size, no programmer will be able to keep the entire thing in their head at one time. That's why the bugs appear.
I have no issue with saying that C is hard to work with in giant projects. If you have an issue with that, write the sections of code that bottleneck in C, and then glue them together with a higher level language (I personally like Lua for this).
Also, the post is mainly complaining about security issues for Chrome. Assuming Chrome is rewritten in Rust or Go, will these security issues vanish? Of course not. Bugs (especially security bugs) will exist in all software, whether it's written in C or Ruby.
So the results of rewriting all C code in the world is: slower, less optimized code and continued existence of security bugs. Sounds great.