It's a good idea not to confuse the concept of a framework with a type or instance of a particular framework. Some argue that because a framework (like 960 for example) doesn't suit a certain use case, you should avoid frameworks altogether. Crazy!
A framework is a tool that good developers use to get a job done. A skilled developer might even build their own framework for their own consumption. Abstraction is a powerful concept that every developer should master.
It's interesting to take a moment to consider a good definition of a framework: "An abstraction in which software providing generic functionality can be selectively changed by user code". It could perhaps be argued that CSS is in fact, a framework extending HTML.
I have played around with 960 and I recommend giving it a go but these days, I tend to make my own set of rules (a framework) using something like sass. There is a port of 960 and blueprint into sass, I think.
I recently worked on a large enterprise website and one of the first things I did was abstracted out the hex values from the CSS into a color palette so there was less redundancy in the CSS files. A month or so later the client asked us to rebrand the site for a different market which meant changing a few sprites and updating the color palette and the job was done. It took just a few minutes!
But to answer at least part of your question: Yes! There are advantages to using a framework. I would even go as far to say that avoiding them is a little naive.
PS: sorry if my answer is not specific but you did mention any insights would be helpful :)