Why wasn't the C-130 adopted for carrier-onboard delivery?

Could the C-130 Hercules have served as a carrier-onboard-delivery aircraft?

It could land on a carrier in trials, but it was too large for practical routine use: it occupied most of the flight deck and could not be folded, lowered, and stored like a purpose-built COD aircraft.

The distinction is between demonstrating a landing and sustaining normal carrier operations. A C-130 arrival would interrupt deck cycles while cargo was unloaded, whereas a C-1 Trader or C-2 Greyhound could be recovered, moved, and if necessary taken into the hangar. A truly integrated C-130 solution would require folding wings and lifts large enough to handle it, turning a seemingly simple adaptation into major ship and aircraft redesign. Aircraft merely adapted to carry mail or cargo also differ from the Trader and Greyhound lineage designed around routine carrier-onboard delivery.