Why? Using them doesn't hurt as they fallback to the text input type. But semantically the code makes more sense as it is more specific, and for those browsers that don't support them, you could fall back on using some javascript to get similar functionality, if you're so inclined.

Of course, these elements will look differently on different platforms/browsers, but for a lot of applications that doesn't matter. Maybe, in the next version/iteration of HTML they make these things a bit more style-able?

They're great on desktop browsers that support them: I get the same widget everywhere, instead of having to deal with stupidly different ones.

You mean "most desktop browsers are fairly useless". Go complain and get them to fix it. Html5 inputs are very old, there is no excuse for "modern" browsers not to support them. It is much better for users if they get the same, consistent date picking widget everywhere, rather than a different, partially working maybe sometimes javascript version on every site.