Unable to replace the standard Rich Text Edit with a custom one in SharePoint 2013

In SharePoint 2010 and earlier the following aspx markup can be used for this purpose:

<SharePoint:RenderingTemplate ID="RichTextField" runat="server"><Template>
               ...</Template></SharePoint:RenderingTemplate>

This markup is usually located in a special *.acsx file under the following folder:
c:\Program Files\Common Files\microsoft shared\Web Server Extensions\14\TEMPLATE\CONTROLTEMPLATES\

This approach doesn't work anymore in SharePoint 2013.
Moreover, nothing happens when either changing the standard markup of the (RenderingTemplate ID="RichTextField") template in the DefaultTemplates.ascx file or even removing the DefaultTemplates.ascx file (from both the 14th and 15th hives).