This is simply not true. It counters any variant of Scizor, for starters, since CB variants can't even 3HKO with Bullet Punch and Sword Dance variants are Roared out. Oh and that's despite a type disadvantage.
Other things it counters are physically-oriented dragons in general such as Zygarde, Garchomp and Dragonite, Excadrill, Mamoswine, Cloyster, Gyarados, most Talonflame variants (again despite a type disadvantage), Swords Dance Aegislash and Diggersby.
Before you say "but it risks taking a random Fire Blast on the switch!", isn't it the same issue with Skarmory, Forretress and physically bulky steel types? The difference between them and Avalugg is that Avalugg can actually do something back with its Ice STAB. Also unlike them it doesn't kill your momentum since it has an actually decent attack stat, a powerful STAB and Earthquake for coverage. None of the things it's supposed to counter will enjoy taking those attacks.
While I may be a bit of exaggerating, I still think it has a hard time justifying itself over other things for a OU slot outside being a lead in HO teams(which he does wonders).
Its SR weakness and pathetic special defence makes it much easier to remove than it seems at the first glance, for this reason alone it is not really some tanks you would rely on. For the same reason it also lost a huge part of its niche as a spinner. It also does not have access to Ice shard, which largely removes its ability to revenge kill, of course you can tank a hit and hit back rather easily, yet again this creates you extra risk that you may not want to take.
In addition, while checking dragons are nice, you would have to compete with the new fairies for that position.
On the other hand, it is important to know that while recover can make its longevity monstrous, its usage does give your opponent free turns. While this is not an issue in general, it can be an issue for Avalugg as it RELIES on it to soak up SR damage, hence making you extremely predictable.
I won't deny however, if you are not facing SR at all, you will have a much better time, as most of the thing mentioned above does involve stealth rock. However by now I still find SR too good for any team to not take.
Anyway, most importantly, don't quote one sentence from my words and rewrite the others. I never say sth about taking random fire blast or the like. And even if I want to say something similar, I would say taking a random STAB special move not being part of its resistance.
Not sure why people would be leaving him in against Life Orb Flamethrowers and Magnezone Flash Cannons. Not everything throwing out Special Attacks is an absolute beast with a super-effective option, and so Mirror Coat is there for the other special-based Pokémon.
Seriously, Sturdy is hardly necessary here (though it might still be his best option). I guess people complain about Swagger Klefki, though, so Own Tempo could be useful there.
Sturdy is a strong option on him as he has access to recover and mirror coat. It is important to know that you have to survive the hit first before you can use your mirror coat, which it won't. And recover allows it to maintain its sturdy much easier.