The post mentions the server is used during the optional execution. My guess as to why would be primarily because there are plenty of curl commands which are impossible to execute via the browser due to browser restrictions and secondarily because the execution is literally running curl, not trying to approximate the equivalent action.

Local execution could still be a handy feature for at least the most common basic commands though, but it'd start to have to wade into "explaining a lot to the user why this isn't really what the result might look like" territory.