Ignoring any privacy implications, terminating https on the load balancer means the load balancer will use more cpu and memory than if it was just a tcp terminating load balancer or working at layer 2. In a lot of architectures, the load balancer may not have as nice of a failover story as the hosts behind it, minimizing state on the load balancer could make state syncing possible for a quicker failover. If you're running load balancing appliances, those tend to be expensive, so you probably want to let them only do what they have to, so you don't need to buy more of them.