The Icebox is indeed a 2-person operation, one person inside the igloo to handle the slip-form and one person outside to shovel snow. Extra people can help to collect snow or swap in. But, you are right, it mainly occupies 2 people, while a conventional igloo can utilize several people.
One important difference is that blocks are made in place from loose snow, so you don't have to pack an area of snow, let it set up, cut blocks, carry them to the igloo, and shape them to fit. Its like casting concrete to build a structue.
One alternative I would like to try sometime is to build a log lean-to in the late fall and cover it with a tarp. The snow would cover it, and viola - you get a snow shelter. You would have to peek in the first time you use it to make sure a bear hasn't taken residence!
A good construction method would be to tie a ridgepole between 2 trees, and lay side purlins against that, keeping the ridge as smooth as possible so the tarp can be laid over it without puncturing. And of course, you need to go back in the spring and take it down and pack out your tarp so you don't leave a mess.
Food for thought. I think the lean-to + tarp would be a lot easier than digging a snow cave or building an igloo, but would be a lot less aesthetic. Digging a snow cave or building an igloo by the conventional method is also a very wet process.