I find I'm in the opposite position - I would rather the date picker is not consistent, because different date pickers have different purposes. The date picker I want to use to put in my date of birth is different to the one I want to use to add an appointment to my calendar, and that's different to the one I want to use to browse prices for different days, and that's different to the one I want to use to be able to select a range of dates, and even that's often different to the one I want to use to select the two dates of a return journey.

Of the classic form controls, choosing a date is probably the one that has the most application-specific needs, and therefore the one that I would most expect to vary between applications.

Yes but companies don’t think that way. Companies have a style that they want to apply to their product regardless of which browser renders it.

The optimal date picker depends heavily on the platform too. Don't want your crusty custom date picker over my platform specific date picker that I know well.

The default datepickers in browsers are not feature-rich at all though. They're fine for extremely basic "pick a date" type of usecases, but as soon as you want to do anything slightly complex like picking a range, a date & specific time in one or having it be interactive in some other way like Google Flights showing you a range of prices alongside the date etc., you have to create your own datepicker component (or use an already built one).

This applies beyond date pickers too. To me, usability trumps consistency when your users access the website across a variety of platforms: mobile vs. desktop, touch vs. mouse, etc.

The default date picker is laughable. For example there is no way to control the format in which the date is displayed.