I like it and, for me, it suits him. I can see how many might find it cliched but I think what makes me accept it is what he actually says. It's in line with how I imagine him.
If he had that gravely voice AND spouted impossibly grumpy and macho lines all the time then it would make me cringe. He doesn't though. He talks in a matter of fact kind of way, from a lifetime of experience, travelling on the road, dealing with all manners of hardship. It's a voice that echos his blunt, grim view of the world rather than a need to 'act tough'.
It's a fine line to walk though and occasionally there might be a slip up. For example, that multiple choice scene in the tavern when he says 'Go away, or I'll kill you', didn't sound right to me but I don't mind as long as those occasions are rare.
I also think his tone is why I find it more amusing when he's being sarcastic or humorous in a cynical way and also more meaningful when he's trying to figure out the morality of his choices.