The pitched lid/top is good, but it's the hinge in a top access nest taht usually causes leakage.Yes top-lifting lids let in a lot of rain.but now that I remember the boxes in drawing ARE exterior and do have a pitched lid so that solves rain issues as long as seams are sealed?( don't know how easy that would be with lid up design) anyway pitched top is good idea IMHO.
Why it's better to have a side access for gathering eggs, and top that is pitched with large over hangs.