First off, thanks for everyone's reply and input.
I asked this question in the first place because of old posts I have read on the forums where people thought the solid bushings at the core support were a bad idea. I was just trying to see if there were some more current opinions. There are also a bunch of old posts out there from people who felt differently. Many said they have used solid bushings at the core support for years and have never had any radiator problems.
Since the radiator uses rubber mounts, I am going to go ahead and use the solids all the way around.
As to why GM didn't use solid mounts, I am guessing rubber mounts were a compromise to please all drivers. A firm ride that might be acceptable and fun to one us might not have been to the average driver.