document.querySelector('#element').style.display = 'none'
That has the same ergonomics as the jQuery selector, and is just a bit longer. I feel like with editors that autocomplete, it's not enough of a difference to warrant the extra dependency.
I've never used JQuery before and would have assumed calling .hide() on an element would set the CSS attribute "visibility: hidden" rather than "display: none"
Nitpick: This crashes if #element doesn't exist, while the jQuery one does not. Also, the jQuery selector is a tiny bit more powerful (:even, :odd).
IMHO, jQuery is good for what it's built for - a nicer interface than vanilla - but the main use case is much less needed now that frameworks exist.
If it's meant to be the case that the element may or may not be present, then I'd much rather see an explicit check for that, than assume one thing and find out another later.