but it is hard to teach them to flush...
Having once had cats, and having had to deal with the "joys" of the litter box, I'd have to say that the cat not flushing the toilet would be a small price to pay to get rid of that litter box.
Besides, there is a possible problem with the cat flushing. Cats, being the way they are, might find it entertaining to watch the toilet flush. And decide that there really is nothing better to do than sit, and repeatedly flush all day long. Running up a sky high water bill, or causing a small flood in the process.