It's not about the range, but about avoiding to close in, because that's risky.

An AEW&C aircraft may reliably detect VLO fighters at let's say 100 km. A F-22 combat air patrol could then escort it and go on supercruise to engage every attacker who's spotted at that distance.
A long-range missile would enable the attackers to shoot at the easily detectable AEW&C aircraft from 150-250 km away, avoiding the risky air combat.

(The figures were just examples, meant to only explain the dynamic.)