What is it about Objecivism that would favor a value system that would result in more of us being our brothers keepers?
First, let me say that I've been on vacation so I apologize for the long delay in responding. As for your question, let me rephrase it slightly...
Does Objectivism hold that individuals have some duty or obligation to care for their fellow man? No, it does not. In fact it states that individuals have no
inherent duty or obligation to any other individual or group. It further teaches that if your desire is to help your fellow man, then you can best accomplish this task through personal investments and personal achievements, i.e., by maximizing your own potential.
For example, Bill Gates gives away millions upon millions of his money to charity and philanthropic endeavors. He can do this because he didn't sacrifice himself to the service of others. We've heard the story about the big hearted charity worker who chose a much lower paying job to be in service to others, imagine if Gates would have done that... Had he set aside his own selfish, personal aspirations and settled for being a social worker, his empire wouldn't exist and the millions of people who benefit from his generosity would be getting nothing. Only the small handful of people he actually worked with would derive any benefit from Gate's sacrifice.
The system appears to be very rational but also cold and uncaring.
The words "cold" and "uncaring" are emotional, not rational. Let's stick with the rational for now. If you want to be as generous and as helpful as possible in the lives of others, sacrificing your own potential is self defeating. In your own personal life, you went to college to become a doctor, that cost a large amount of money, a huge investment of your time, hopefully you saw rewards fitting for such an investment. You could have forgone college and spent that time and money on some charity and, as a result, had a much lower paying job to support yourself.
The Altruist would appeal to your emotions, cheer your decision and laud you for sacrificing your own potential to the good of others. The Objectivist would appeal to your rationality and point out that maximizing your own individual potential opens up opportunities and abilities for you to help your fellow man that simply aren't available to you if you sacrifice yourself to the good of others.
Altruism is emotional, irrational, it teaches the individual that self sacrifice is a moral duty or obligation. In contrast, Objectivism rationally explains that self sacrifice is counterproductive, that whatever it is you wish to accomplish in life (even if it's being your brothers keeper), you best accomplish your goals by maximizing your own individual potential to reach your goal. Just as we cannot tax our way into prosperity or spend our way out of debt, you cannot fulfill your own potential by sacrificing that same potential to others.