You are right the basic design of the helmets is to reduce acceleration forces on the head and BRAIN by increasing the time of impact.
There are hardshell and softshell helmets. Generally the harder helmets are designed for kids, or perhaps some sports like BMX. In that case, the thick shell may spread the force further around the skull. I presume the foam is also different, so from your example, foam designed for a 1" impact radius from the hammer may be different from foam that spreads the impact out to 6".
The helmet industry has been studying different types of impacts from a direct impact flat surface to an impact on a wedge shaped surface. And, the need for one helmet for all potential impacts.
The net over foam helmets from a few years ago apparently seemed like a good idea, but had a side-effect of being more sticky on some surfaces causing torsion stress. Fixed by both a slick surface over the helmet, as well as the MIPS and WaveCell helmets.