> Smaller nuclides have higher total binding energy than the large nuclides
i.e. total binding energy literally goes down as you get to larger nuclides.
> That doesn't contradict every step inbetween being favorable.
Yes, it does. Energy is strictly additive.
> You are adding hydrogen with zero binding energy.
Exactly. You are taking a bare nucleon, with zero binding energy, adding it to a system, and reducing the total binding energy (i.e. increasing the potential energy of the system). By conservation of mass-energy, this requires you to put in energy, and increases the total mass of the system.
i.e. total binding energy literally goes down as you get to larger nuclides.
> That doesn't contradict every step inbetween being favorable.
Yes, it does. Energy is strictly additive.
> You are adding hydrogen with zero binding energy.
Exactly. You are taking a bare nucleon, with zero binding energy, adding it to a system, and reducing the total binding energy (i.e. increasing the potential energy of the system). By conservation of mass-energy, this requires you to put in energy, and increases the total mass of the system.