Probably it could have been done with Cr(III), but making complexes of Cr(III) is not that easy. Chromium complexes are very inert, so starting off with a chromium (III) salt is no option. Ligand replacement is very slow for them. The same problem exists for cobalt(III).
But, such complexes usually are made by starting off with the metal in the +2 oxidation state, and then oxidizing it, with the suitable ligands present in solution. As the metal is oxidized, it is coordinated at the same time. And here is the main difference with chromium and cobalt. Cobalt has a very stable and easy to handle cobalt (II) aqueous cation, which only is oxidized easily in the presence of suitable ligands. Chromium on the other hand is very hard to maintain and keep pure in the +2 oxidation state. Solutions of chromium (II) are such strong reductors, that they even may produce hydrogen gas from water. So, working with chromium (II) as starting point requires special precautions (such as inert atmosphere), while this is much less of a problem with cobalt.