Pressure Plate Carpets

I love decorating my builds with carpets, especially using them as doormats at entrances. However, when I place a carpet there, I lose the utility of a pressure plate to automatically close the door behind me. My suggestion: A craftable "Pressure Plate Carpet". The Craft: 1 Carpet (any color) + 1 Pressure Plate. The Function: It looks exactly like a standard carpet but acts like a pressure plate (emitting a redstone signal) when stepped on. This would allow players to have functional, auto-closing doors without ruining the aesthetic of their entrance.