The only reason I can think of to use JQuery beyond that is that it's a dependency for a lot of libraries you use, you're supporting something other than Android/iOS on mobile or you really, really like the extras like animate, their powerful event system, extend and/or their ajax methods.
That said, it's popularized a lot of useful coding methods, showed everybody how normalization should be done, and demonstrated the power of closures/factory functions to keep objects very light-weight in spite of having a ton of functionality associated with them. It's not just for client-side-illiterate noobs. Studying JQ under the hood can teach a lot about JQ.
The newer JS libraries/frameworks/tools are concerning themselves more with how to implement highly complex UI in an app-maintainable way.