I wonder if we should just make native date inputs the default for 4.0. HTML5 date input support has gotten much better with evergreen browsers and not having to support multiple selectboxes would let us save some complexity internally as well.

I am fine with making native datetime inputs default in 4.0 and dropping the selects altogether. In practice most sites/apps use JS based pickers anyway for better consistency and usability.

We should retain the array marshalling for datetimes for backwards compatibility. I bet somewhere someone is using array dates in an API.

Keeping datetime array marshaling sounds reasonable.

So should I reopen this against 4.x instead, with the helper and widget code for selects removed?

I think that is a good idea. We could move the old widgets into a plugin that folks can use if they really need that behavior.

I prefer using dropdown to select the year for birthday, which can allow to select "9999" for the year if someone prefers not to say his year of birth. Therefore for birthday I like the select dropdown version.

Adding this as opt-in sounds reasonable for 3.x.
Also keeping the old one (if we switch over), even for 4.x, as opt-in would be nice.
Many still use that actually.

I like using Tiny Datepicker (https://github.com/chrisdavies/tiny-date-picker) where possible but my clients prefer picking the year of birth in a dropdown where I can add the year option "prefer not to say" oder "unknown" in my web based contact relationship management system.

I think year, and month inputs could stay as select boxes. The native HTML inputs are better for date and time values though.

If we are going to switch to native inputs then by default they should be used for all available types. There's no HTML input for year so keeping the select box for year is fine but there is one for month so for that native input should be used.