Earlier quoted context omitted.
That's not quite correct, is it? Consider shooting at a bird. A falcon travels twice as fast as a pigeon, but you don't need a bullet that is twice as fast to shot the falcon. You simply adjust the lead distance when you shoot at the falcon. In your argument you assume that you need to cover some distance in the same amount of time, but you don't need to. You simply lead the target a bit more. As for detection time,…
Agreed, it all depends on the use case. If you are trying to hit an evading target, you have to be faster. If you are trying to deny the ship from a destination, you don't.
Dealing with evasion is a whole other matter. A stationary iceberg can hit a ship that tries to evade if it does so too late. Conversely simple error in your knowledge of a ship's position and velocity can cause it to be miles away from where you expect it later in the journey.