Concerning the mixing, it cannot be zero. A zero means simply there must be a symmetry behind it. But data is the queen after all. So if data tells it's small, it's small.

One further question (without any real answer) which this could lead to is the following: How come it is so small? This is indeed very unnatural: we like parameters of order of 0.1-1.

The quick answer is that there must be some mechanism behind the entire setup that makes the mixing tiny. And this is where it starts to be tricky (and funny too)... Designing such a mechanism.