If you just destroy the whole thing, it's much simpler and probably less expensive. It was probably all obsolete anyway.
I'm not sure that's true; if you destroy the entire computer, how do you verify that the important parts (e.g. the hard drives) were actually destroyed and not repurposed? Presumably they were inside the case, but if you don't open the case up and look, you can't prove that they weren't pilfered the night before and are in someone's bedroom now, waiting to be listed on eBay or somewhere worse.
If I was that paranoid, I'd want to manually inventory each hard drive and watch it being fed into the shredder with my own eyeballs.
My suspicion is that most parts of the computers weren't destroyed, but rather they were sold off or given away to some third party that will figure out what to do with them. But it's easier and simpler to tell the public they were destroyed.