This is actually simpler than you think.
Candidate Smith has 3 nominations.
Candidate Jones is on his slate for the Congressional Nom. and wins the appointment. Charged
~ Candidate Smith is still in the running before they hit the national pool because they have Sen. A and B.
Candidate Brown is on Sen. A slate and earns the appointment via WCS. Charged.
~ Candidate Smith still has Sen. B before they hit the pool.
Candidate XYZ wins Sen. B. Appointment. Charged.
~ Candidate Smith is on their way to the pool....wait!
Candidate XYZ declines the appointment and now Candidate Smith with the 2nd highest WCS is charged.
You need to understand charging to understand why 3 nominations help you when it comes to appointments.
It is true the more slates you are on, the better, but there are states like VA, MD, CA, TX, NY that are notorious for only offering 1 nomination. It does mean that someone with 3 nominations in another state is more competitive it just means their MOCs don't talk!