Timezone support, no date ranges (eg from-to), date formats are a mess (mdn: "At the moment, the best way to deal with dates in forms in a cross-browser way is to have the user enter the day, month, and year in separate controls, or to use a JavaScript library such as jQuery date picker."), often rules are needed (eg only weekdays), non gregorian calendars, ...

A good date input would cover at least like 80-90% of use cases in my opinion. From experience it's currently more something like ~40% or so.