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They are hard to intercept because ballistic missiles follow a predictable arc. It's not a matter of requiring more computing power, it's a matter of the defender not knowing the "true" trajectory ahead of time. Like, as soon as the missile changes trajectory, the calculations can be done in a fraction of a second. The issue is, the interceptor vehicle should have been launched 3 minutes ago. So the calculations aren't the problem, the problem is that you'll be running out of missiles and the time to launch them. Computing power is cheap. Getting a kinetic kill vehicle from sea level to the edge of space? Expensive and takes a hot minute.
This is a different matter from hypersonic cruise missiles shot and flying within the atmosphere. The Kinzhal used against Ukraine is essentially an Iskander missile but launched from the air. A defensive missile takes seconds rather than minutes to reach it, and at the velocities involved it can't pull tight turns for evasion. And the missiles would be much cheaper than exo-atmospheric kill vehicles.