Here's the issue: Each one could apply for the trip with 7 hikers. But if they name alternate leaders that identify others applying for a trip, their applications will be removed. So... say one or two who apply as lone leaders actually win their trips with 7 slots.
...Then when it comes time to go on the trip, life gets in the way, people drop out for various reasons, they don't feel ready, someone gets sick, etc, etc. Now dropping members isn't a problem, UNLESS one of those dropping is the one named as the trip leader.
You see, the trip leader, identified on the lottery application, is the ONLY person who can pick up the permit to hike. Identification is required. Inyo doesn't allow adding alternate leaders onto a permit, so they won't allow the permit to be reassigned to another person.
So there you have the problems and kinks that can come up. How you play the system is your business. Good luck!