How to inspect HTTP requests in Safari 8 or later
Actually, there is a way to do that, just like Chrome:
On the Inspector window, at the Resource sidebar (at right), there's a small arrow at the "Request Data" subsection. That's where we need to click!
(Sorry for the browser language in Portuguese, btw).
Once the data screen is loaded, you can even switch between Request and Response views.
Hope this helps :)
The only solution I found, was to use the Timeline and select "Network Requests" on the left. Click the red "Record" icon, so that you record all your requests. They will then appear in the timeline viewer. Then make sure that you select this time span (scrolling inside the timeline shows a smaller or bigger time span), an the request will appear below the timeline viewer.