I am wondering if I can adjust the grid width to what I need, for example to "stretch" it to 1400 on the 1440 screen
Sure, do whatever you want with it.
I know by now that the 960 grid is the most common, but why is it so, when screen sizes are so different?
Because people are lazy.
It's common because it was/is a nice easy framework that designers and developers can use to throw together a layout using a pre-existing grid system without having to worry about both the design of the grid itself and the technical implementation of that grid (i.e. the HTML/CSS).
If that works for you... great.
Time is money, so saving on design time, development time and having a common starting place for both designer and developer (assuming they're different people) is great. But it is a shortcut and isn't going to work for every design and (as evident by your question) isn't going to fit evolving screen sizes. A static grid of any size isn't really an ideal solution any more and you should really be using some form of responsive grid if you're working for any general web project....
Long story short, don't rely on any pre-made grid system just because it's popular or easy or anything else. Creating a grid system should (in an ideal world) be as much a part of your design process as anything else.