I agree on the consistency part. Even if you need several (max 4?) other libraries to do stuff like AJAX and Promises, it would still be consistent. If you want and need, you can always add a small wrapper around those libraries and add consistency to the API calls.

Staying current is, in my situation, a luxury I can't afford. We have a web project using third party libraries and UI Frameworks which depend on JQuery. As the project is complex and already has a lot of code, kicking JQuery out is not an option (or, at least, neither trivial, nor quick). I'm sure this happens often with legacy software.