I think this only counts in the simplest of cases? Such as serving HTML straight from memory.
In other cases there are various micro or macro services to call to, state to communicate on the enterprise service bus or something equivalent, separate database servers to run queries on, etcetera. A single request might hold up several other requests due to badly-thought-out dependencies between services and physical servers. More servers wouldn't scale exactly, and it might be difficult to find out where the next bottle neck is.
And if some external bottleneck exists... that's a separate issue and adding more servers isn't going to solve any problems at all.
I guess I still just don't see it... I know servers don't scale "exactly" in the sense that one service will require another server before another service does, but that doesn't make it nonlinear. It just gives it variance (fluctuating both upwards and downwards) around a line. It doesn't turn it into a curve.
If you already have a load balancer, you should be able to scale on the server part from 1-100 exactly linearly. Where are your extra 7-10 coming from?
And if you already have a database, you usually just upgrade its specs linearly too. And if god forbid you need to shard... that's perfectly linear too.
For pretty much all practical planning purposes, servers do scale linearly. The equations you're describing seem to imply a deeper hierarchy of server connections, but that's not usually how it works -- servers (whether load balancers, web servers, or databases) just come in bigger pools, not trees.
Where are you getting your log() or sqrt() terms from? Is it some kind of application-specific caching layer or something you've used in the past?