You are vastly underestimating AES-NI. Most modern Intel CPUs can handle that kind of encryption throughput (when paired with fast enough memory). Even my old Sandy Bridge-E CPU from 2011 gives me ~96 Gbps of AES throughput (with quad channel memory).
http://arstechnica.com/security/2013/12/we-cannot-trust-inte...
I'm not really sure how this would work for network traffic, I guess for disks I would expect CBC mode, which would require an IV? Is that right?
So could the hardware be made to expose the key, or IV's, or leak information in some unexpected way?
Perhaps feasible, but far far less likely than compromising the entropy of a random number generator.
You can setup IPsec tunnels on your application nodes and use that to get transparent encryption of all traffic, but that is pretty complicated to configure and manage. It's much easier to just have your different applications use an encrypted and authenticated transport when talking to each other over the network, whether they are in the same datacenter, or talking to a remote datacenter. This is how Google and Facebook do their cross datacenter encryption.