https://gitsense.com/rapid-browsing-1.mp4
And this is an example of bulk diffs browsing:
https://gitsense.com/rapid-browsing-2.mp4
You can find the source for the chrome extension at
http://github.com/gitsense/insight
And the Git indexing engine at
Edit:
It may not be obvious, but for the second example, I'm clicking the right arrow to quickly iterate through the diffs.
For the diff, this is done in realtime with https://github.com/Microsoft/monaco-editor
Also my product isn't really dependent on GitLab or GitHub. It works in standalone mode as well.
For what it's worth, features like that (along with, say, line-by-line staging) are the reason why I usually use a GUI client and only drop down to the command line when necessary.
Something even closer to what you're asking for... in github hit the 'history' button on a file (next to blame) and you'll get the commits which affected it. Hit the 7 character commit-id and you'll be taken to the diff of that change, jumped specifically to the file in question.
The history button in github is close to what I'd like, but it's not quite as friendly as single next/previous buttons that just paginate the changes to a file. That makes cycling through the history very easy, whilst 'click commit id, back, remember which commit we just viewed, click following commit id, repeate' all sounds a bit painful.