I had an experience to use current limiting reactors with high impedance in the power distribution system of oil refinery complex. In conclusion, I decided to use fault current limiters instead of current limiting reactors, which cause voltage instability of power system.
When I conducted power system studies (Short Circuit Currents and Load Flow Studies), voltage profiles could not be maintained within the acceptable level due to high impedance of the reactors (it requires over 20% of impedance), and it did not allow satisfactory active power flows due to excessive reactive power losses.
Of course, it is no doubt that using CLR is a good option to reduce short circuit contribution, however CLR application shoud be carefully considered by conducting short circuit current calculaitons, load flow studies, etc.
In addition, I believe that main concern of CLR application is voltage dips under various operating conditions as already posted by "jbartos"