I feel like anyone who lived through 1999-2006 feels the answer to "Do we need jQuery" is a strong yes.
Of course, we could remove jQuery.
What jQuery does is make life simpler for developers (as well as resolve a lot of cross browser quirks so developers don't have to think too hard about that). What that blog effectively advocates is the reversal of the number one rule of programming "be lazy". Functions and methods are reusable for a reason.
For an app as broad and as complex as ours, replacing jQuery with vanilla javascript isn't really viable. We have tens of thousands of lines of javascript code which will multiply into millions without reusable compact methods.
For a single page website, you probably could just about tolerate it, but honestly I question the effort even then; other than to feel happy as you sip a soy latte while stroking ones hipster beard before adding "Built with ❤️ in vanilla Javascript" in the footer.