Litter boxes with doors

I got the jumbo Catit litter box with the door.  I ended up taking it off because my 4-ish month old kittens didn't seem to understand the door and one got in and then was just sitting in there and I wasn't sure if it wanted to be there or if it couldn't figure out how to get out. 

Should I wait a week and let them get used to the box and then put the door on or just forget the door?  I don't want to take any chances that they'll reject the box.  Does the door really help contain the smell (I clean the box daily so I'm more talking about the smell when they take a fresh poop, not smell from the box itself).  Does the lid without the door contain the smell?

I also took the filter off for now because it seemed like it was just going to end up getting chewed up.

Most cats don't like doors on boxes.. they can't see out and they don't see it as a clear escape. I'd leave the door off.

We got a box like that for our newest box, but the cats only understood the door as part of a toy rather than a litter box (we introduced it to our older cat empty). Eventually the door broke off and both cats are used to uncovered boxes, so the filter, door, and top became essentially useless to us. Between all the cats I've met, all of them have preferred the open boxes where, as @Draco mentioned, they can see and be more aware of what's going on around them.

Thanks.  So far they're using it a lot.  I have 2 other boxes with the other litter they use next to it.

This is my second try with clumping litter and I swear it stinks more than the non-clumping clay.  So weird.  I'm going to give it a couple days because maybe I'm imagining things.  But with non-clumping, I definitely would prefer the open pans because they're easier to clean, and I dump them every other day or so.

We have a large, covered litter box with a swinging door on it and the only issue has been our youngest hiding in there until the oldest walks by and diving out on him  LOL

Serious tho, living in an RV, I had to have something that contained as much of the litter as possible.  Our oldest was an outdoor stray so he kicks litter to the end of the earth and back.  They both seem to have no issue going as often as they were with a lidless box.

Our cat will only use a covered litterbox; our last cat didn't mind an open box, but normally used his covered ones. I've never used the swinging doors or filters, because I believe they both trap odors inside, making it more unpleasant for the cat(s).

Interesting, Jcat.  I'm surprised at how little the are using the other 2 open boxes.  Maybe mine prefer the privacy of the covered box too