Why even use wheels when you can reinvent them? I'm not saying there are no reasons to go "bare metal", but satisfying your developer ego is not one of them. Unless you need every inch of performance or control, jQuery (or alternatives) is probably the more reasonable choice.
jQuery wouldn't be created today in anything like its current form. It still lives on largely because of inertia. Using the APIs provided by the browser is in no way reinventing the wheel!
A lot of the commenters here have a very old school view of jQuery. They seem to believe that if you're using jQuery, then you must also be employing manual DOM manipulations, manual state management, etc.
You can implement modern component-ized front-end architecture while still using jQuery. My company built an in-house front-end framework heavily inspired by React and Vue. But instead of abstracting away from the DOM, we've embraced the DOM by utilizing DocumentFragments for highly performant rendering. When our components render, they return regular ole HTMLElements.
The components built using our framework work with or without jQuery. No manual DOM manipulations, one-way data binding, sane state management, templating, child components, state triggers, etc. A lot of us use jQuery simply because we prefer it's compact and expressive syntax.
As long as you're using recent versions. The whole point of jQuery is that you can write some code and be sure that it will run correctly in older versions of the browsers.
No it doesn't.
Browser incompatibilities are basically a non-issue these days for 95% of projects. Animations etc are far better done with CSS than jQuery (particularly when it comes to hardware acceleration). The Fetch API works in every browser. So on and so forth.
I think the OP wasn't suggesting that "managing" without jQuery is difficult. Certainly, I can say that I haven't touched jQuery in years and haven't looked back once. There's nothing I miss.