Ask HN: Why does DNA have only 4 nucleotides?

I was eating with my dad, who is a biophysicist, and he brought up an interesting question for which I haven't found an answer. I thought maybe someone on HN would have heard something more.

Why, after billions of years of evolution, do we still have ALL known organisms still have 4 nucleotides? Yes, Uracil is used in RNA but it encodes the same information, ie why is it always base 4? How come a 5th nucleotide has never appeared, or any nucleotide become less prevalent?

It seems interesting that the genetic code is base 4. And are there really only 20 amino acids?