Why is the input to an activation function a linear combination of the input features?
The main reason is that a linear combination of the input followed by a non-linearity stacked on top of eachother is a universal function approximator. Which means that no matter how complicated the true underlying function is, a neural network can approximate it to an arbitrarily small error.

There's also the efficiency factor since a linear combination of $n$ inputs each having $m$ dimensions can be represented using a single matrix multiplication $h=X \times W$ where $X$ is an $n \times m$ matrix (where each row is an example and each column is a feature of that example) and $W$ is an $ m \times d $ weight matrix. And computers are VERY efficient at doing matrix multiplications. Thus, the more you build your model to use matrix multiplications the better.