Your value isn't just the code you write. One of the biggest benefits you have (presumably) is that they can easily communicate with you and might even be able

Your value isn't just the code you write. One of the biggest benefits you have (presumably) is that they can easily communicate with you and might even be able to meet in person. Frequent communication and the ability to manage expectations is why you can justify $100/hr or more. You're not just providing them with code; you're providing them with confidence that you are a low-risk option.