For one, their documentation has consistently been accessible to beginners. Other frameworks might have had some crossover functionality, but Jq wrapped it all up in a neat, concise, package complete with a supportive community and excellent documentation that takes away the intimidation for new entrants.
Anyone who has written an 'Ajax' connection call in JavaScript can attest to the relief it has brought on that front alone.
DOM manipulation within your scripts, without having to patch together different libraries in an unreadable mess is nice too.
I've done limited things with the tool, and I can see its benefits clearly - maybe because I see the tool as a curated forest, where those packages you mentioned are like scattered, but awesome in their own right, trees.
Forgive me for the short response, I'm on a phone.