Ed Nelson had demonstrated in his book Radically Elementary Probability Theory
that a good part of probability can be made clear to freshmen without appealing to measure theory by using the Mises frequency approach. There are other gains for various courses. But above all nonstandard analysis allows students to understand better the triumphs and tragedies along the path of mathematics. Our ancestors Wallis, Gregory, Barrow, Newton, Leibniz, Euler, Cauchy, and many others were geniuses and to try and understand their ways of thinking is much better than to arrogantly accuse the great masters of being second rate thinkers in any style similar to that of Kline, for instance: "The net effect of the century’s efforts to rigorize the calculus, particularly those of giants such as Euler and Lagrange, was to confound and mislead their contemporaries and successors. They were, on the whole, so blatantly wrong that one could despair of mathematicians’ ever clarifying the logic involved." We learn math to fit life, and infinitesimals are part of the life of humankind.