On the majority of aircraft fitted with arrestor hooks that were not naval aircraft designed for landing on carriers, this couldn't be done for the simple fact that the hook was not strong enough to restrain the aircraft within the space a carrier aircraft lands at. The arrestor hooks on non-carrier based aircraft were designed to restrain the aircraft on airfield emergency arrestor systems that don't provide anywhere near the strain capability of carrier arrestor systems, bearing in mind that they're located on long concrete runways that provide plenty of rolling distance once the aircraft's movement has been arrested.
A wee pictorial representation of what we're dealing with. This is the arrestor hook on the Lightning, the boom is less than half an inch thick. In the picture with the hook, the drag chute stowage door can be seen.
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This is an A-4's arrestor hook. Even though the A-4 is smaller and lighter than the Lightning, it's boom is beefier.
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For comparison, this is an F-4's arrestor hook. A mite more substantial given the Phantom was a bigger beast, but the point is obvious.
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