Why are so many cats white underneath?

According to a recent documentary I saw on this, its about a 'shortage' of pigment DNA in the cat.. Pigment DNA causes the fur to be black or ginger or whatever other colour. White fur has little or no pigment in it. So when the colour pigment runs out, the remainder of the fur is white

In the domestics (moggies) the gene for white is in there DNA. It's a dominant not recessive gene, which means it's easily passed on to it's progency. White fur is no harder to keep clean than a darker color, but it's easier to see the dirt. A cat with no white will get as "dirty" as a totally white cat, and will spend hours grooming the same as a purely white cat will do.

A cat hunts in low light conditions and their prey mostly has poor eyesight and sees in black and white. An entirely mono-coloured cat would appear darker on its underside because of the effects of shadow, and being silhouetted against the night sky when viewed from slightly below - its prey are small critters like mice etc. looking slightly upwards. Having a pale or white belly counteracts the optical darkening that occurs and the cat better blends against the background, while any pattern on the fur on top - stripes or patches - help break up the obvious feline upper profile while it is creeping up on prey.

It's just that most cats that are no breed domestics of any colour/pattern carry white DNA. That's why it's VERY seldom to see a solid black cat without a small patch of white or even just a few white hairs.