Technically SIPER interceptors (block i/ii) can shoot down AShM.
However, interceptors that meant for long range and high altitude is not economically feasible for point defence.
That is why every country including Turkey has more cost effective medium category of missiles for point defence like (HISAR-N, ESSM, sea captor, BARAK-8)
And secondly, SIPER interceptors are not quick reaction missiles. Which usually have TVC or altitude control thrusters to quickly direct it to the targets, this saves few second and this is critical given short reaction time after missiles appears in the horizon.
ESSM, BARAK-8 VL-SRSAM and ASTER-15 all has TVC.
Sea captor, G40 has altitude control thrusters.
Even though HISAR-N doesn't have any of it, still it can direct itself toward targets relatively faster than a SIPER interceptor.
Between long range high altitude interceptors and CIWS there has to be medium range interceptors like ESSM or HISAR-N.
Otherwise, you have to use expensive SIPER interceptors for point defence when enemy cruise missiles appears in the horizon, (which also not meant for quick reaction) or wait until those missiles gets within range of CIWS. Which is uncomfortably (and dangerously) close and increases the probability of taking a hit.
@Anmdt
Maybe when SIPER block ii is inducted you model would be more effective as I suspect SIPER block ii (without booster) would have same reaction time as HISAR-N.