From my understanding, the primary benefit of the Hypersonic Missile over the ICBM is not the speed of payload delivery, but the amount of warning given to the target. An ICBM needs to ascend 100s of kms, thus enabling it to be detected by very far away radar systems. Those same radar systems that would be over the horizon at the lower altitudes within the atmosphere. Launching an ICBM almost immediately announces to the world "I am launching a nuclear warhead", thus enabling countermeasures to be readied, and a retaliatory strike to be launched. The time between this warning and the strike is indeed small (measured in 10s of minutes), but that's much more time than a hypersonic missile gives.
And the maneuverability - if you just adjust the course slightly ten seconds before impact, at these speeds, that’s a big difference. Ballistic mostly just falls down, i.e. you know what it will hit when you observe the launch (somewhat simplified).
Missiles since the 80s or so don't just fall down. The discontinued Pershing MARV could perform 25G maneuvers/corrections and was radar guided and had terrain mapping.
Well yeah, hence "(somewhat simplified)". One is a lifting body that control its flight path and can decide whether to strike or to just keep flying for another 1000 miles, the other can slightly adjust its falling down path and wobble enough to hopefully confuse countermeasures.
