To the best of my knowledge, there are no i7 chips with 8 physical cores. i7's typically have 4 physical cores and create 4 additional virtual cores with hyperthreading. The statement that you have 8 cores is only true in some circumstances.

As your question indicates, LinearSolve uses the Intel MKL library. Intel indicates that hyperthreading will generally not be useful in this case. See the hyperthreading section at this website. This section is especially relevant:

Note: If the requested number of threads exceeds the number of physical cores (perhaps because of hyper-threading), and MKL_DYNAMIC is not changed from its default value of TRUE, Intel MKL will scale down the number of threads to the number of physical cores.

Therefore, Mathematica appears to be solving the problem in the most efficient way, and doesn't seem to want to be forced to solve the problem in a way that will likely be less efficient.

It appears that your chip only has 4 cores according to Intel. It can create 4 additional virtual cores with hyperthreading, but virtual cores and physical cores are not always equivalent. The statement that you have 8 cores is only true in some circumstances.

As your question indicates, LinearSolve uses the Intel MKL library. Intel indicates that hyperthreading will generally not be useful in this case. See the hyperthreading section at this website. This section is especially relevant:

Note: If the requested number of threads exceeds the number of physical cores (perhaps because of hyper-threading), and MKL_DYNAMIC is not changed from its default value of TRUE, Intel MKL will scale down the number of threads to the number of physical cores.

Therefore, Mathematica appears to be solving the problem in the most efficient way, and doesn't seem to want to be forced to solve the problem in a way that will likely be less efficient.