> You will still need libraries to do nicely formatted time strings like "next week" or "3 hours ago"

If you want those formatted values to be consistent with the rest of your app, you will need this anyway.

You app does support localisation right?

Also: there’s no guarantee a browser would have the same localisation as your app (for instance German-language browser, English website).

You really have to do this 100% yourself in your app if you want the result to look right.