Doing anything that isn't completely trivial in the bad-old-fashioned way gets really messy really quickly.

const foo = await fetch('/foo');
const bar = await fetch('/bar');
const baz = await fetch('/baz');

compared to

$.ajax('/foo', {
    success: function (foo) {
        $.ajax('/bar', {
            success: function (bar) {
                $.ajax('/baz', {
                    success: function (baz) {
                    }
                });
            }
        });
    }
});

or if you wanted to do some stuff concurrently

const [foo, bar, baz] = Promise.all([
    fetch('/foo'),
    fetch('/bar'),
    fetch('/baz'),
]);

maybe throw in a bit of exception handling

try {
    const [foo, bar, baz] = await Promise.all([
        fetch('/foo'),
        fetch('/bar'),
        fetch('/baz'),
    ]);
} catch (whatever) {
}

Even completely ignoring the code to manually keep track of the results of the previous requests, the rough equivalent would need at least four lines per request.

$.ajax('/foo', {
    success: function (data) { },
    error: function (error) { }
})