I'm just a little angry how you think cats can be treated like dogs. I can only assume you're as angry with have had cats do their pooping and what not in your garden. If so I'm sorry to hear that. My nan had trouble with cats digging up her bulbs =/. I hope you, and all others find better and more practical solutions though
Perfectly reasonable thing to do - when we had cats that's what we did. We had a large shallow container of dry builders' sand in the open lean-to where the logs were stored - it stayed dry and was accessible to our cats whenever they were outside and they used it.
Our neighbours said that our cats did not use their gardens and they certainly did not use my flower beds or veg garden. The sand was changed regularly and it was no bother. It would be helpful if all cat owners did a similar thing and encouraged their cats to use it.
By their nature it might not prevent cats from occasionally pooping elsewhere, but it helps control the problem if they know of somewhere suitable outside that they can use, just as they use the cat litter indoors.
If they're empty cover them with a boards, slates, tiles etc for the moment. When they're full of plants and well watered the cats won't be interested in them.
Yup. My cats always try to find an empty spot in the soil. Also I think cats dislike gravel.