Depends on what kind of plastic. Most of the hard plastics like ABS and polystyrene are subject to breaking or shattering if the impact is energetic enough. If your case was made from puffy polystyrene like packing peanuts, it would probably survive at least one impact, but it wouldn't be too durable in the long run.
There's a reason rubber is used for things like tires and vibration isolation, rather than plastic.
I'm not too sure about the types of plastic used for the hard cases, but I know neoprene rubber, sillicone, and TPU (Thermoplastic polyurethane) are often used for the soft cases.
The plastic cases definitely seem like they would be more brittle and prone to cracking, but would they prevent impact energy transfer to a phone during a drop/hit more effectively?
The case itself breaking wouldn't be a problem as long as the phone doesn't get damaged, I'm more interested in how much shock energy would get to the actual phone with the different materials.
Plastics like ABS and polystyrene are very commonly used to make cases for phones, calculators, etc. There is a long history of using such materials and they used to be fairly cheap to use in manufacturing, but since the basic ingredients are made from petroleum or natural gas, plastics like ABS and PS have become more expensive in recent years.
IDK how much shock energy is transmitted to the phone mechanism. I don't think the manufacturers know or care either. They make money by selling you a new phone periodically. Adding new features to the basic phone also helps to create a demand for new phones, and there are many people who must have the latest gadget. The days of having a phone company install a basic handset which would last for decades are gone for good. It's a disposable world now, baby.
There may be some shock-proof phones available. They probably wouldn't look too sleek, though.