Well, web workers are great but they are intented to be used for computational expensive tasks which are CPU bound, because tasks like those are the ones that can block your UI thread and ruin UX by freezing application completely until CPU bound tasks are not being resolved.

On the other side, I/O operations handled by javascript async execution are concurrent and by the nature of Event Loop they will not block UI thread because once call is stared it will be immediately offloaded from UI thread, until resolved, and like that async call will never be blocking for application UI - meaning there is really no any significant benefit if you decide to move async execution to dedicated worker thread via web workers in javascript.