first of all, most modern sites are using “synchronous” ajax, that doesn’t means they freeze browser by specifying “synchronous” flag to XMLHttpReuqest, but rather they follow the following steps:
onSomethingEvent -> Display “Loading” -> Make request |||||| Recieve Response -> Update Interface -> Hide “Loading”.
That’s what actually make them “SynJAX”, and that’s the problem which must be solved with “A” in AJAX, and not what Jeff writes here.

second problem, is synchronization of events. If you won’t block user with “Loading” dialog, you should handle concurrent request to the server. Let’s get back to the “check marks” sample in the article. Let’s assume you make really “A”JAX request to the server on each click. If user clicks too much and too often, there is a possibility to get out-of-order requests on the server due to network latency. I.e. your server may receive updated states in the following order: 1: enabled, 3: enabled, 2: disabled. This must be handled carefully, and solutions is not always trivial.
And that’s the _main_ problem you don’t often see the real part “A” in modern web sites.