This is one of those basic UI things that are missing/bad in native HTML controls, and why we end up having to implement this stuff in JS.
90% of the annoyance could've been dealt with if they had just chosen a default date value of, say, Jan 1960 or so.
Maybe the real solution is a simple explanation for how to use a date picker component. It'd help those users not just on this site but on many other sites in the future.
Tbh I don't really know what improvements could be made to the picker itself. It looks pretty consistent with the implementation of most other browsers and OSes and even most native components I've seen
I'd love to hear actual thoughts on improvements though