The Chinese numbers are already in use ages ago and (as far as I know) predates the Ming dynasty. Fun fact, there are both “upper case” Chinese numbers (壹，貳，叁，⋯) and “lower case” numbers (一，二，三，⋯). The uppercase numbers are still used in official documents, esp. monetary ones such as checks to indicate the monetary value. For example: “壹拾贰万叁仟肆佰伍拾陆元整” means “¥123,456”. According to Wikipedia, this is done to prevent the numbers from being doctored, like changing 1 to 7.
It’s true that the lower case numbers aren’t used as much, but they are still used in text when the number is less than ten, e.g. “I have three children” -> “我有三个孩子” as opposed to “我有 3 个孩子”, for better paragraph consistency, typesetting and whatnot. However the Chinese numbers will become too long for anything greater than a hundred, so it’s all Arabic numbers after that.