Hello Borja,
If you go back to the mathematical definition of assortativity, it makes perfect sense. It is a normalized correlation. If all degrees are the same, then the correlation is 0, and so is the variance, 0/0 -> NaN. If the degrees are *almost* the same, then the correlation is almost zero, the variance is nonzero, verysmall / nonzero -> verysmall.
Intuitively, your regular network is not special among networks with the same degrees: the vertices have no choice but to connect to other vertices of the same degree. Compare with networks with a wide range of degrees present: some of these are assortative, some aren't. Unlike in the case of regular graphs, there's a freedom.