Let's see... 151 Pokemons, 12 Alolan Forms and 18 Mega Forms. All in all, that will be 181 Abilities, of which some are the same while having different priorities.
We have 11 Players and Brock. Everyone got 4 Pokemons at the start. [12 * 4 = 48]. So hypothetically there should be 133 Pokemons available at the Safari Zone if we play with all Pokemons. Drac already counted the amount of Pokemons available: 62 Pokemons, which is less than half of all Pokemons available.
Considering we are playing with 11 Players and can rank 10 Pokemons... Well, long story short: Pokemons who don't have two people ranking it are going to be rare.
One strategy is to not care about the Rankings at all, not filling in the Rankings, and get a random leftover Pokemon though.
But since everyone have to go for their three most wanted Pokemons to unlock their Trainer Ability... It might be difficult to get the three without "Trading" after all.
And then there's the question of what will happen to the "discarded"/"freed" Pokemon... Oh well. I will see it soon enough.