And as far as "not targeting old browsers" there are plenty of places where modern browsers differ and jQuery normalizes their behavior. Chrome doesn't support mouseenter, Firefox doesn't support focusin, Safari's String.trim() doesn't trim zero-width spaces, their CSS uses prefixed properties, etc.
Also, talking about jQuery in isolation is like talking about C++ without its runtime library. One of the strengths of jQuery is its ecosystem such as plugins.
That said, I've always found jQuery's function naming to be particularly ambiguous. There's no indication that "find" searches an element's descendants for a matching CSS selector based on its name. On the other hand, vanilla JS's element.getElementsByTagName is so much more verbose. Back in the day I found PrototypeJS [0] to be much better organized and offer the same feature set, but it's largely fallen out of use since Rails dropped it. mootools is nice but the docs, while comprehensive, are arranged in no logical order. Every time I try to pick up mootools I end up running around the docs in circles.
tl;dr jQuery is overblown but I think there's room for improvement over vanilla JS.
Plus there's always the (literally) hundreds of plugins for every possible application of jQuery.
I'd love to see a JS library that doesn't try to add a lot of functionality, but only decruftify the browser API.
The right aim would be to end up with a complete API that might actually replace the normal JS api (DOM+otherwise) in actual browsers.
var elem = document.getElementsByClassName('foo')[0];
elem.fooBar();
elem.foo = 'bar';
rather than $('.foo').fooBar();
$('.foo').foo = 'bar';
even if you don't know anything about writing optimized JavaScript code.However, jQuery's main feature is having a nice interface that is much more consistent and usable than many of the native APIs. The "fluent interface" or "method chaining" style is especially nice.
A modern, more minimalist alternative would be a nice thing, but at the moment I think jQuery is probably still a good bet for simple cases.
You can also mow your lawn with a pair of scissors, which is about like doing anything non-trivial in the browser without jQuery.