Why does a filter need to be applied to the output of the input gate before cell state is added to?
Here is my hypothesis : The $i_t$ can add explainability to the model, as the value of the sigmoid function can give an idea as to how important a particular word is to altering the cell state $C$. This is because $i_t$ lies between 0 and 1. Having single $W$ do both filtering as well as a feature transform of $[h_{t-1},x_t]$ not only puts more stress on the matrix (has to do two things at once), but also no longer has this explainability factor. 

Example: 2 vectors may require the same transformation $W*v$, but unless you allow seperate sigmoid function to give each an importance, their contribution to the cell state will remain same.