Look at <select multiple> for example—the browser built-in is borderline unusable. Anything that requires combining a click with the shift and ctrl/cmd keys is not going to go down well with the average user. Same goes for <select>s that need more advanced behaviour like filtering. There's <datalist>, but it's incredibly basic and pretty useless for most cases you'd want that sort of input.
The web is an app platform whether we like it or not, and I'd like to see a robust set of browser-native controls with mechanisms to customise styling and behaviour. It would improve accessibility, improve performance, reduce page sizes (because we wouldn't be re-implementing the whole world in JS), and it would at least go a little way to offsetting the slow erosion of quality desktop software that web technologies are bringing.