Just an additional thought to my original post to add. Perhaps the big reason that Nihilus is a key point of frustration is that he feels like he has everything going for him and no weakness to exploit. With Sion you can turn his pain/suffering debuff against him since it buffs your damage, while Traya you can topple or exploit Stand Together or Bonds of Weakness, so they feel like there's some kind of weakness to hit.
But Nihilus? He gains protection when you hit him with basics, which almost all teams need to do regularly simply because cooldowns are a thing on every other move, and damage to his protection is essentially wasted. Like all STR bosses, you can't debuff him unless they're unresistable debuffs. Hitting him makes him faster, which makes it harder to plan turns, which is particularly awful considering he's the one you need to do that against the most. Buffs other than Foresight are much less effective or arguably a liability against him, since he dispels on basic, gains the buffs he dispels himself, and on top of that also reduces the cooldowns of not only Force Drain but Annihilate when he does so. He ignores your protection, cutting the durability of most characters by more than half just innately. When he Force Drains, he increases your cooldowns, likely forcing you to use more basics on him, feeding him more protection. And on top of all of that, he has Annihilate, which now not only instant-kills with no chance of revive, but gives him a huge buff, so if someone gets hit with that, you definitely want to restart, as it will massively reduce your run's total.
And what do you get to fight back with? Unbreakable Will, which basically exists solely to let you survive Annihilate. Unlike Sion or Traya, there's no way to use this as a weakness of Nihilus' that will let you do better, it just helps negate one of his many strengths (albeit the most overwhelming of them if it didn't exist, granted).
Seriously, notice that the teams that do well against him are only those that exploit effects that do damage based on the health percent of the boss - JTR with expose, and to a lesser extent Deathtrooper with Deathmark and that one thermal detonator team. These same abilities do well against all STR bosses, because of the health bloat of the raid - it's just that nothing does better than them against Nihilus, because he has no weaknesses to exploit, and seemingly every advantage going for him.
In contrast, in phase 4 he's more manageable, because Traya and Sion's mechanics are in effect, and Bonds of Weakness in particular being exploitable by the Nightsisters helps make it more possible to fight him effectively (albeit not without many of the same frustrations brought on by his many strengths). But on his own, in phase 1, there's nothing like that, only things that work entirely to Nihilus' favor.