... and remember that in most controls, if not all, you will be asked to take off your shoes before you can go anywhere.
edit: my comment is for cleated shoes. If you ride on non-cleated shoes, then you do what you want.
OOI, what about MTB/touring shoes with recessed cleats?
There's still enough flex in the sole that the cleat can contact the floor when walking in them. I hear the occasional tell-tale click/scratch sound when I'm walking in my various MTB/touring shoes, especially on the tiled floor in the changing rooms at work.
Cleat covers (for LOOK style cleats) aren't entirely reliable too, they can easily fall off.
The simplest option is to ask for all cleated shoes to be removed.
I never worried about my socks getting wet or dirty at controls, they got wet/dirty enough out on the road and I generally had a clean pair to put on for each day.