Oh we already know this. There are parts of the genome that, if even slightly changed, cause terrible, terrible things.

Mutations can happen anywhere, but serious mutations (that may affect the basic things a cell needs to do in order to exist) result in cell death and therefore don’t manifest in the population — the population continues on as though the mutation had never existed.

In this way, natural selection conserves some parts of the genome while less essential parts can vary more freely without being deleterious to the organism.

For example, most non-bacteria (including all plants, animals, fungi, protists) have special proteins called histones. Histones are used to package the DNA together and wrap it all up. Cells can’t function at all without a these proteins, and the most important histone proteins evolve so slowly that they’re almost identical between a human and a pea. (Humans and peas shared a common ancestor over half a billion years ago.)

ETA: My molecular biology knowledge is rusty, but IIRC the way DNA is packaged and unpackaged can also reduce or increase the risk of DNA being exposed to potential mutagens. So if it’s wrapped up, it’s harder to access and tamper with

What OP said is Motoo Kimura's Neutral Theory of evolution. There's a lot of evidence supporting it. The vast majority of mutations have a negligible effect on fitness. So it is very possible that something may evolve purely by chance.