One benefit of turning wooden eggs is the sheer practice of tool control it requires of the turner. Yes, the first few eggs will be a scrambled mix of mistakes. (Sorry, I couldn't resist the pun.) But at least you are practicing with small bits of wood, and not wasting larger blanks.

Eggs can be turned with just a few tools. For me the most useful tools are a spindle roughing gouge, spindle gouge and yes, the skew. Some other major benefits: Eggs can be turned on any size lathe, and they don't take very long to complete.