I really wish we'd gotten a couple more useful native controls back when there was any will to add that kind of stuff... It's sad/annoying to see all this reimplementation of simple stuff like comboboxes, and then all this extra effort to make it work OK in different form factors... The great experience of the select element that just gets you a mobile appropriate native UI for free is unavailable for so many simple cases.
Last I checked the form additions from HTML5 were still pretty spotty in support, several don't really have a real world use case, and nobody wants to make any more really.
The "problem" with native controls is that they might visually clash with the design of your website. That's why everybody implements their own controls or uses libraries like jQuery. And sadly, that's probably why we don't have good default controls.
That requires the ability to style things like the dropdown of the combobox (e.g. to add rounded corners, change the background/border colour), and the rows for each items (e.g. adding padding, and divider border styling). At the moment, that is difficult because they are not part of the HTML box model. And what about styling controls like date input or colour pickers?
Another issue is styling checkboxes to use custom images for the different states (including hover and pressed styling).
Last I checked the form additions from HTML5 were still pretty spotty in support, several don't really have a real world use case, and nobody wants to make any more really.