SPDs can be clear of the ground, depending on your shoes.
I use SPDs with Specialized Cadet (discontinued) and Giro Rumble shoes, which are fully recessed. I walk a few km a day in them, and have been known to run in them. On a perfectly flat surface the cleats don't touch the ground when walking on either of them, but they often find bits of grit or uneveness in the ground, which can make them sound like tap-dancing shoes. The only time the cleat is even close to a problem for grip is on tactile paving, especially if running.
Dirty cleats will always risk dirtying carpet; after oiling the clipless mechanism of my pedals I'm very careful to avoid wearing my SPDs on carpet.
With the M424 pedals I use, I've had to file a bit of the plastic cage off; if you had similar pedals and thinner cleats you might need to remove more (though the Cranks Brothers Mallets seem to have grubscrew studs you could remove).
Here's a picture of the cleats on my Giro Rumbles, showing the 2 mm that the cleats are clear of the ground, and just how much rubber would have to wear away to reduce this