> It appears you need the energy from 3 in order for the 2 to make a bond.
> It's the other way around. Two atoms alone will release a bunch of energy when they form a molecule; exactly enough energy to rip the molecule back apart. That energy has to go somewhere, and where it goes is the third atom.
In other atomic physics experiments it's a problem - three-body collisions are able to dump energy into one of the three atoms and that atom has enough energy to escape the trap. These are "three-body losses".
Whereas with two-body collisions, neither atom can be going any faster afterwards than the fastest one was before the collision. So they remain trapped.
Since the three-body collision rate is proportional to the cube of the density of atoms, and the two-body collision rate only to the square of density (for obvious reasons), this phenomenon limits the density of atomic clouds we can do experiments with. If we increase the density to the point where three-body collisions are significant, we rapidly lose atoms.