Once a while I use such a debugging to examine the loading steps of my first screen. I can record and replay the actions created by initialization code and network requests.
Also in my tool I got a diff tab to show the changes of the store, so I can check if that code worked correctly.
Also, histories are useful too. Like some server pushed messages, I can find them there.
Time traveling debugging may help in large apps. Small apps could be simple enough and one does not need a tool to understand it.
My tool was a bit different from Redux, you may check this: twitter.com/jiyinyiyong/status/737188000174481409