Imagine you're loading a profile page on some social networking site. You fetch the user's basic info, and then the information for N photos, and then from each photo the top 2 comments, and for each comment the profile pic of the commentor. You can't just fetch all this in one shot because there's data dependencies. So you start fetching with blocking IO, but that makes your wait time for this request proportional to the number of fetches, which might be large.
So instead, you ideally want your wait to be proportional to the depth of your dependency tree. But composing all these fetches that way is hard without the right abstraction. You can cobble it together with callbacks but it gets hairy fast.
So (outside of extreme scenarios) it's not really about whether async is abstractly faster than sync. It's about how real developers would solve the same problem with/without async.
(Source: I worked on product infrastructure in this area for many years at FB)