Looks like Record Type Selection page doesn't work consistently for all objects when New button is overridden. For e.g. it works fine for Account (i.e. record type page is skipped), when new button is overridden with a lightning component. But, the issue persists and the record type selection page is not skipped, when new contact button is overridden with another lightning component.
I could also see that there's a known issue but this is only specified for custom objects at the moment: https://success.salesforce.com/issues_view?id=a1p3A0000018AqwQAE