'Aligning items' as a general principle can help designs and layouts look the same, but even in a design that fits into a 4, 12, 16, or 24-column grid there may only be one or two edges where the alignment matters anyway.
The reason a 12-column grid is more popular than an 8 or 10 columns grid is because of the variety of ways it can be divided: into columns of 1, 2, 3, 4, 6, or 12. A 24-column grid would be even more flexible, but more things to count.
My suggestion is to toss out the 'grid CSS' and design with a grid in mind, but just make the divisions look good. Sometimes in a web layout some things are fixed width (like a sidebar) while other parts of the layout are fluid and can expand - so especially when making responsive design look good, only loosely follow the idea of a grid :)