An interceptor does not have to be as fast as the target that it is intercepting. An interceptor with a speed of mach 2/3 can even intercept a hypersonic missile with mach 8 speed because Interceptor missiles do head on collision with their target, and not chase it. This is why.
From my knowledge. Interceptor missiles don't need to be as fast as the missile/target they intercept but they have onboard computers which can predict the general direction of the target and it only has to travel at that point because it knows that by the time the target reaches the point, the interceptor will hit it too. So what I am trying to say? Missiles with a more predictable flight path will be much more easier to intercept.
That is a misconception.
The interceptor doesn't need the same speed as the target, but the higher speed, the better.
Intercepting is not like two bullets heads on flying in the straight line, it is one missile to hit another one from the side. Unfortunately modern ground based commanding computer couldn't tell you the hitting position in the moment of collision precise enough, so the interceptor need the seeker on board and keep adjusting her own trajectory. These adjustments consume your time of intercept window. And don't forget today's target missiles will maneuver in their final stage. So, there is a very good chance the interceptor will miss the target if it is too slow.
2 or 3 Mach won't be suitable for today war, you can still use it, but success rate will be very low. That is why Americans, Russians and Chinese really work hard to make their interceptor faster.