DOM inconsistencies aside, a big advantage jQuery has over native API is that it is just as easy to work with multiple elements as it is single elements.

Modifying your example:

    var d = document.querySelectorAll('div');
    d = Array.prototype.slice.call(d);
    d.forEach(function(el){ el.classList.add('new') });

Vesus:

    $('div').addClass('new');