RAW he can be an unstoppable killing machine against lightly armored single-wound infantry.
I believe this is
RAI too, however, because the Bone Giant has a very similar rule but different wording that makes it clear the Bone Giant can only pile in + attack on extra time per combat phase:
Colossus of War: After a Bone Giant has attacked in the combat phase for the first time roll a dice. Add one to the result if a Necrotect from your army is within 18". On a 5 or more, that Bone Giant can immediately pile in and attack for a second time that turn.
(underlines added for emphasis)
It's almost the exact same: model attacks in the combat phase, roll a
D6, and then model has a chance to pile in and attack again. Since
GW has proven its ability to write a once-per-turn additional pile in and attack rule, I believe they intended Konrad to be a hilarious anti-infantry blender, and the "any attacks" wording of Konrad's rule is deliberate.
If one plays it that way, here's the math:
On average he'll inflict ~3.1 wounds vs. 5+ save models (assume you're only re-rolling 1s to hit), which means roughly 1 in every 3 combat phases will see him attack again (rolling a 1 or a 2 after inflecting 3 wounds). If he does, and inflicts 3 more wounds, it's 5/6 chance of getting off a third round of attacks, at which point you can remove the unit without any further rolls since he'll have unlimited attacks and pile-in moves until there's nothing alive within 3" of him.
Against elite infantry and/or multi-wound models (like stormcast), it's not as grim: he'll cause an average of 2.4 unsaved wounds vs. a 4+ save, meaning red fury usually won't even have a chance to trigger against 2-wound, 4+ save models. Even if he kills 2 models, that's still a 1/6 chance of triggering the second round of attacks.
Tying Konrad up with multi-wound models and/or high armor saves is the order of the day (or just dropping grudge thrower rocks on his head...). With a 5" move and not much else going for him defensively, that shouldn't be too hard.
As an additional balance point, this isn't all THAT different from attacks like Gyrocopter's steam gun that can potentially hit/wound every model in a unit. Deadly against single-wound infantry mobs, uninspiring elsewhere.