Cats are Terrible Gardeners

I have never been able to keep houseplants. My house is plagued by cats who devour any leafy material that passes through my door.
Despite this, I've been possessed, for a couple of years now, by a fascination with fairy gardens. I really really want to keep one of those cute miniature landscapes. I figured that if I made one planted with cactus the cats wouldn't chew it.

They don't. Instead they pull the cacti out of the soil. I think they're jealously defending their sunny window sill from vegetal squatters. These cacti are proving pretty hardy but I can only replant them so many times before they suffer. I just can't win.