"Thing with longer beak can reach things it likes to eat better than thing with shorter beak, even if it is just 0.01mm longer each generation" is hardly "billion-to-one odds mutation".

That's like saying "tall people tend to have tall kids, and dwarfs tend to have dwarf kids? Billion-to-one odds! Billions-to-one! Tiny asian parents have seven foot tall black kids all the time, the odds of a tiny asian parent having tiny asian kids is zero! ZERO!". Longer-beaked birds tend to have longer-beaked chicks.