Distributing the player mats
It's really simple, actually:


The rules say


  Randomly shuffle the the Faction Mats and Player Mats



Do they say "shuffle a number of mats equal to the number of players, starting with the lowest ranked mat"? No, they don't. If they wanted you to do it so, it would have been written there.


You bought the game. It's your property.


Think it would be better using the lowest ranked mats? Do it, it's your game, you can do whatever you want. Or you can go for a bidding, even. Or you can directly allow people to chose their faction mat -like we always do, so to try different factions every time. Or you can stop someone on the street to chose one for every player. Or maybe give all the players the same faction.

Luckily there is no law preventing you to experiment with a game that you own, and luckily the game will not self destruct after the first play. Do whatever you want, and if you don't like the outcome do it differently the next time you play. Simple, right?