It's pretty routine for a CI integration to test every patch, yeah. Not all do. (e.g. Gerrit-based systems generally do because the unit of review is a single patch, github likes to do integration on whole pull requests). It's certainly possible. I don't really understand your point. Are you arguing that it's preferable to dump a giant blob into your source control rather than trying to clean it up for maintainability?
No, I prefer small meaningful commits. I am not for or against the index. I have no problems switching my brain between git add -A or -p as necessary. Like you said, it happens too often that someone sends you a huge pile of code (C code, in my case). My first impulse is to build and run it immediately. For me, just compiling the code can take up to an hour sometimes. Running my full test suite takes even more hours.
At some point I am ready to craft this code into multiple commits. After my first git add -p and git commit, I don't know if HEAD is in a state where it even compiles. It takes further work and discipline to produce a whole series of good commits.
And I was saying that as a practical matter, you don't always get that option. Individual developers working on their own code don't need the index. But then quite frankly they don't need much more than RCS either (does anyone remember RCS? Pretend I said subversion if you don't).
Situations like integrating a big blob of messy changes happen all the time in real software engineering, and that's the use case for the git index.
I split work consisting of multiple changes in the same file just fine under CVS and Quilt.
I would convert the change to a unified diff, remove the change, and then apply the selected hunks out of that diff with patch. ("Selected" means making a copy of the diff, in which I take out the hunks I don't want to apply. Often I'd just have it loaded in Vim, and use undo to roll back to the original diff and remove something else.)
Using reversed diffs (diff -uR) I used also to selectively remove unwanted changes, similarly to "git checkout --patch"
This is basically what git is doing; it doesn't require the index. The index is just the destination where these selective hunks are being applied.
