It's the opposite; it would be easier for people to catch up. By providing more funding for health, housing, and education, more people would have the opportunity to become wealthy themselves, and to do great things for society. How many potentially great developers are lost in awful educational systems, for example? The U.S. is supposed to be land of opportunity, where the belief is that anyone can thrive given liberty and opportunity, and that talent does not depend on the wealth of your parents. Right now, college education is determined, more than anything else, by parental wealth or income.
If you mean that it's harder for other billionaires to catch him, it's kind to consider their welfare. But as Gates would pay more tax than the other billionaires, they would catch up to him.