Why have a 'egg' base station with an RF transmitter to a sensor board? How about a sensor board with Wi-fi and no second board i.e. the egg?

It isn't critical to have a user interface for sensing air quality. Neither is it critical to have an "egg" as part of the design or concept whatsoever, inside OR outside. However, this is a project that is far more important for its impact bringing together people into a community and giving them a way to participate
directly in this process than it is for simply "crowdsourcing data". It's the stringing together of all of these elements that is really special about what we are doing here -> funny, warm Egg visual; tactile and personal interface inside; citizen science; crowdsourcing data; community-designed.

Additionally, there is a technical driver here as well. The experience around setting up a Wifi device that has no screen/UI is not very good. It would have taken some serious extra development to solve this problem. Companies like Electric Imp exist solely to attack this issue. It was much easier for us to use a very simple and cheap RF system to make the Egg plug and play rather than trying to build a wifi experience.