- All current blades are not a constant-pitch helix. This would be needed for them to fit inside each other.
- Careful thought would need to be applied to balancing the propellers given the slight difference in the sizes of the pairs of opposite blades. The masses need to match, obviously, but so too would the moment of inertia, lift and probably drag.
- The blades could not be variable pitch, except when fully extended.
- The blades would have to have a constant cross-section.
- Your [it-won't-work-because] goes here...
Postscript 3 March 2019
A similar alternative that I thought of after I wrote this article is to have each blade telescopic and retractable inside itself. This would allow odd numbers of blades and probably be simpler overall (and certainly more symmetrical).