Think also that in a night watch deck, Val + TLS + Dolorous Edd = 8 cards every round they are alive.
Anyway, not having claim in the intrigue challanges is not the end of the world. You get power through unopposed and you can trigger effects by winning, like Fury of the Sun, Cersei Lannister, Condemned by the Council or Wars are Won by Qills.
In the next series of chapters we will see the new plot that searches a maester. So having Maester Aemon from the beginning will absorb one military claim per round. I'm an aggro player and i'm a little worried about that, but I will not say that this will be boring.