Cersei does, and who, with a lick of sense, would ever trust her? Taena Merryweather lets Cersei molest her and grope her in bed, spies on her liege lady and prior benefactress and even divulges secrets which could ruin her with her husband...but she temporizes and hedges and refuses to bring her own son within reach of Cersei's grasp, when most mothers in the realm would have leaped at the opportunity for their child to enjoy the patronage of a queen. Once it becomes known what lengths you might go to for your children's sake, no one with any brains would trust you after that, because who can say what threat to your child you might feel compelled to avert, or what benefit for him you might see by some double-dealing at a critical time. And in a medieval setting like the Seven Kingdoms, you can't make it on your own. You need allies to help protect your stuff from the covetous, you need followers to support you or lieges to protect you and if you can't be trusted, why should anyone follow you when you might shaft them of their rightful benefits or rewards to protect your children. Why should your lord protect you when you might default on your taxes or services owed to him, because you wanted to save that wealth for your kid or wanted to stay home and protect your kid rather than help your lord.

In hindsight people give Robb crap for "riding off to conquer the Riverlands" rather than staying in Winterfell to protect the North from the Ironborn and the Others, but at the time, they were no threat. His own grandfather WAS being threatened - besieged in his castle no less - and his uncle was a captive. If Robb would not bestir himself to save his grandfather and uncle and lift the siege of the castle in which he himself had been born, why should his vassals trust that he would protect them? Why should future allies he seeks trust that he would come to their aid for a peace treaty when ties of blood could not induce him to come to the aid of the Tullys?