Six yolks in a bowl: Why not optimal circle packing?

The system doesn't try to minimise the radius of the enclosing circle, but its potential energy. We can idealise this as non-overlapping disks in a convex rotationally symmetric potential $V$ with $V(0) = 0$. The configuration that was physically realised then has potential energy $5 V(d)$ (with $d$ the diameter of the yolks) while the configuration from Wikipedia would have potential energy $6 V(d)$.

Those packing rules only apply for rigid circles. Anyone who's ever cracked an egg knows that yolks are not rigid. As a result of that, you can clearly see that the sides of yolks are flattened as they touch another yolk.

So those packing rules simply don't apply.

What do you mean, "the yolks don't follow optimal packing"? Sure they do. The configuration with one yolk in the center has the exact same radius as the one with six yolks distributed along the edge.

It also has lower potential energy, thus the 6-circle solution you cited is a non-global optimum at best. In fact it's probably metastable, given egg yolks' general tendency to be squishy blobs instead of perfect circles.