Why would anyone think that it would get linearly worse? What's the (wrong) assumption there?
But I suppose the question is underspecified. How does the load balancer know which systems are busy? What happens to a request if the load balancer routes a request to a busy server?
I think that the issue is in part due to the variables. Plotting the mean request time is less intuitive than plotting throughput.
If you plot throughput vs number of servers, it'll be a straight line. And asking people that, I think most would agree on a straight line. But who knows!