Well, if the ultimate 'point' behind life on earth is to disperse and retain specific genes, the fact that we live in a highly mutagenic environment makes it statistically improbable that any single gene will persist unaltered for any long period of time. They will change according to the environment and the proclivities of the organisms housing them. So, rather than being the actual gene that is being preserved, perhaps it is more accurate to say that the 'point' of life on earth is the persistence of DNA as a molecule. Unaltered, unbound, non-coding, just a 'simple' protein found in every living thing. The information that is 'written' by DNA using genes changes over time but the actual language of this writing does not. If a gene is a word, and DNA is the letters, we see that words can change but the letters do not. I would imagine that the unchanging element here, DNA itself, is of primacy rather than the words it creates.
Bear in mind, I have very limited understanding of biology but find it interesting.
If the genome (/DNA) of organisms was left unchanged, then evolution couldn't take place. As counter-intuitive as it sounds, mutations actually aid survival in the long term. You have to remember that sexual reproduction produces an organism with different genome than its parents. Miosis (the cell devision mechanism which produces sperm and eggs) purposefully produces cells with different genetic makeup than its parent cells - as opposed to mitosis, the usual cell division in an organism, which produces cells with identical genome.
Mutations over time change the genome of an organism, but that only harms that particular organism, and it usually manifests later in life, after it's reproduced - in the form of cancer for example. Mutations and miosis allow for daughter organisms to have different genetic makeups, and as such (on the big scale) allow for natural selection to take place.
What you say about gene survival is debatable. If there was
random selection, then individual genes would have little likelihood of survival (assuming mutations etc). However, the mechanism for evolution is natural selection: organisms with appropriate genetic makeups can survive and reproduce (again, on the big scale). That means if a particular gene is beneficial for said organism in its environment, then organisms with that gene will be more likely to survive and give offsprings. While less beneficial genes will be slowly eliminated because of mutations etc (because organisms carrying it will reproduce less likely).
Evolution is a fascinating subject IMO.
E: I may have misunderstood you. Your understanding of the DNA structure and its purpose is correct: the basepairs and whatnot is like letters, and the sequence is the "words". Obviously the structure doesn't change, only the sequence (similarly to proteins). However, gene is a sequence of basepairs, and that sequence is what is responsible for the properties of that gene. That is what changes.
In that sense, the structure of DNA and RNA is universal on Earth - every known organism has the same structure of their DNA and/or RNA (albeit different sequences) - but that also holds true to some degree in the case of proteins. There are a little over 20 proteinogenic amino acids, and it's pretty universal throughout life on Earth.