I think people are tired of predictable plots where an orphan, who is secretly the chosen one and/or a prince, predictably saves the day in the end.
I don't think ASOIAF is grimdark, but it wouldn't have been as popular if the plot was the following instead of everything that occurred during and after Eddard's beheading:
The North rides down to Kings Landing to save Eddard.
A large battle scene occurs with Rob getting injured and they're they lose and have to retreat.
Tyrion who was mainly there to provide comic relief, reveals Jon Snow is the real Targaryen heir.
Jon Snow, through some deus ex machina, finds some Dragons and rides south with the army to defeat the Lannisters.
Everyone lives happily ever after and Jon becomes King.