Their misfortune becomes yours. Differing rates of growth don't go away. The rate at which a given company is growing is deeply embedded in their processes, marketing, inventory, sales channels and public perception of their product line. You can't merge companies with highly different rates of growth without exposing many fault lines in the combined organization. Synergies are not an accounting trick.
Synergies run deeper than keywords on paper.
Vastly different organizations cost big money to merge, and up-front estimates of synergies can be expected to be extremely optimistic. It wouldn't be sick otherwise. Cray had some cool technologies when SGI bought them. The trouble was, many were no longer relevant as microprocessors increasingly grabbed the supercomputer's traditional space. Digital's Alpha seemed like a good prize, but Compaq instead focused on Digital's service network as the real prize and offloaded the Alpha onto Intel.