It is actually wired to except a child to be disciplined. Kids will do what their mind will trigger, they are brainless. Making mistakes is obviously a common face of life. We learn with time.

Tell us whether it is worth making concessions to children.

A very simple rule, if your kid made a mistake and since you punished them (which is actually not accurate, it is important not to take any such inhuman acts not even smallest punishments. One, teach them the right way with politeness, once twice or thrice. Two your little angel is stubborn and now you are punishing them, by not allowing them to watch cartoons) and if they are sorry I truly believe they deserve to watch Cartoons then.
Rare case your kid know how to play too.