This is very true! How often do we keep ourselves from success because we do not let things happen? We do not take risks. We do not open ourselves up to new ideas. We get in our own way. There are many things that we do to not let things happen.
Although I think the line in the play was meant as a reminder to let the good things happen, it can also be a reminder that bad things can happen if we let them. For example, our health may suffer if we overeat, do not eat a healthful diet, do not exercise, do not manage stress or if we smoke or drink excessively. Our professional and personal relationships will suffer if we neglect them. Our career will suffer if we do not continue to strive to improve.
Keep in mind that “Anything can happen if you let it”—for good and bad! So let the good in, and keep the bad out.