We've had a Litter Maid for our two cats for at least 5 years now. It's the LitterMaid Plus version. Don't know if they still make that extact one or not. We're still on our first one. It does not completely ellimate you needing to clean the litter box, but we only have to clean it about twice a week... once midweek to clear out the waste container and add a little litter and garbage day we do a more thorough cleaning.
Don't just use the plastic boxes that come with it for the litter container. We put a plastic garbage bag in the plastic box and then swap those out. Over time the plastic boxes eventually break and you still need to replace them, but I think we've only ever needed to buy one package in all the time we've owned it.
Yes, it's still a litter box. Some residue will stick to the blades and the very bottom of the pan. But it's not a daily chore anymore. Ours is in a spare room, so the little bit of litter outside the box doesn't matter and we just peridocially vacuum. But otherwise, unless they've just used the box, I don't really notice the smell. (Or if we've skipped the midweek cleaning and the box is full enough the cover doesn't close, you can smell it a little.) I know when we bought ours, they did have a little tent cover that you could get to contain the litter, don't know if they still have one.
With two cats, we do still have a second basic litter box with a cover, but they hardly use it, mainly use the LitterMaid.
We've generally been using the ScoopAway multiple cat formula litter and have had good luck.