Personally I have zero success using critter keepers- it caused a chinese mantis male to become SEVERELY deformed during a molt(he didnt even successfully molt actually and got stuck because he tried molting on the floor because he couldnt climb) and disabled my ghost mantis female's ability to climb.
Over the years, I've had very good luck with Krit Keepers. However - as mantisfan101 mentioned above, it's imperative you put your mantis in larger cages as they molt. It currently am raising Tenodera Sinensis. As they outgrow each container, they are moved to a larger container (about 3x molted length high). This can be an expensive proposition for some. I have large and the very large sizes for L5 through adult molt. Yes, one or two sides should be modified with screen/mesh for climbing to hang upside down off the top.
Here is a current picture of Photon in her Kritter Keeper. She molted very successfully hanging from the top. The sticks were removed prior to her molt.
I think it can work, especially for smaller species and at least one gripping surface other than just the lid of the cage. I've had budwings and even s lineola successfully molt to adult in them.