Those JS pickers are going to be needed for a long time still, because native widgets are a nightmare to style consistently. Apparently nothing has been learned from the <select> styling minefield of the past.
I don't think that everyone should be able to edit the style of native elements.
I prefer a consistent behavior, and the select itself works fine everywhere for example.
But i sadly agree, JS stuff is going to be needed for a long time.
There are good arguments for styling native elements and against them. I don't think this is specific to the web, cross-platform GUI toolkits have had this challenge forever.
The current datepickers on the desktop are "consistent in the same browser across many sites". There is no native solution for "consistent in the same site across browsers", which makes a lot of designers and PHBs upset, doesn't always fit the overall look of the site, and makes it harder for developers because each browser brings its own quirks with formatting, localization, validation, etc.
But i sadly agree, JS stuff is going to be needed for a long time.