The proposal doesn't fix JSON it introduces an entire new format. One which I would not be able to use without a 3rd party library that parses it. If I'm already using JavaScript that is one of the many benefits it has in the first place.
Timestamps are easily included when I want them, I tend to prefer UNIX time as it's just so much more impact proof. With this proposal can I use UNIX time if I want?
I don't have any problem with JSON. If I did I would have a problem with JavaScript itself, and while there's plenty to complain about I wouldn't propose mixing more formats into it as a solution. There isn't enough care being taken not to introduce additional complexity into the JavaScript world.