What is the purpose of the Gennaker girth rule?
The gennaker girth rule : at least 75 % of foot length (SF) at midheight (SMG)
Is it to prevent the sails from being used up wind?
Yes. Of course you can try to use a gennaker upwind, but I believe the rule it to prevent someone optimizing it for upwind; then you'd see some very odd "spinnakers" come out on light air races.
