First, "the most natural thing in the world" has nothing to do with morality. Humans have the ability to reason, so we're able to look past our natural instincts and find the truth.
Second, I agree that having the option to be moral is a great sign of societal progress. I think shaming immoral people is now an effective evolutionary strategy. Social outcasts are less likely to reproduce. Survival of the fittest is no longer about who has the most food(at least in the us). It's now about which culture values reproduction the most is we're looking at the macro scale and usually vapid things like attractiveness on the micro scale.
Saying that "reason" necessarily trumps natural instinct is naive. Your assumption is that your limited experience, knowledge, and cognitive ability are superior to the sum total of all human and animal experience and cognition throughout the aeons.
In group preference and mutual concern exists because it is stable and robust. Even if it doesn't give an optimal utilitarian outcome in the short term, it is capable of perpetuating itself. There is not a single society in history based on purely altruistic principles that has ever survived. Reciprocity is necessary.
No, I'm saying evolution has no reason to take morality into account. In fact, humans evolved to be immoral, if we weren't greedy we'd die. We are no longer in that situation. Being moral had a negative correlation with number of offspring. Arguing that the sum of people greedily trying to survive somehow means being greedy is moral now that it's no longer necessary makes no sense. There is not a single society in history that has had computers other than ours, so I'd say we're in unprecedented times.
I think evolution does take morality into account in a certain way. If you're a utilitarian, in one formulation, you'd say that the good is people being able to satisfy their desires. People form groups, build things together, etc., in general, to satisfy their desires collectively. We are able to satisfy more desires by working together.
My point is that barring genetic engineering or drugs or something else causing us to change our motivational system fundamentally, there will always be some people that are a bit greedier than others. Even if we are collectively materially rich, there are always more things to be acquired, and even if we had unlimited material wealth, there would always be scarce goods like the time/attention/respect of others.
Would you, for example, advocate that one should spend their time with others that they don't like, or even people who behave abusively, as long as these people get a lot of pleasure out of the interaction?
On your second point though, people generally do act morally, and that moral behavior is an evolved trait of a group, because moral behavior promotes the interests of the group. Compared to, say, 50,000 years ago on the savannah, the amount of concern that people show for one another's well being is far higher.
I really don't think people generally act morally at all. Instead I'd say they generally act in a socially acceptable way so as not to become ostracized. Then the question is how well do social norms line up with ethics. Overall it's pretty close, but there are clear areas where social norms are not ethical, such as eating factory farmed meat and donating to domestic charities instead of ones that target the global poor.
Second, I agree that having the option to be moral is a great sign of societal progress. I think shaming immoral people is now an effective evolutionary strategy. Social outcasts are less likely to reproduce. Survival of the fittest is no longer about who has the most food(at least in the us). It's now about which culture values reproduction the most is we're looking at the macro scale and usually vapid things like attractiveness on the micro scale.