The amount of support you need for it.
- TTar for support on a Choice pokemon designed to switch in and out? Yeah, Pray your opponent doesn't have Stealth Rock down too. Hippowdon walls the both of them.
There's nothing wrong with T-tar. He and Azelf both take neutral from SR, and if it really bothers you bring a spinner. He's weak to Ground, which Azelf is immune to, and Fighting, which he resists, so few if any people will be using those those moves against him. So what's left? Surfs from Starmie? Starmie takes 92.76% - 109.21% (172 HP Neutral) from U-turn, so if it's coming in to spin or as a counter, all you do is switch to Blissey, if it's still alive, that is. With SR down, and most good teams do carry it, you have a guaranteed OHKO and they just lost their spinner. Milotic? 252 HP/136 Def takes 32.49% - 38.07% from U-turn and 46.95% - 55.33% from Return. Hippo? Takes 27.38% - 32.38% from Return (less that 25% with U-turn), so switch to any decent fast special sweeper with Ice Beam and he's KO'd or at least forced to switch, and with U-turn your switches do not lose a turn.
-Dugtrio sucks as a switchin on fast U-turners.
Why should he? As long as you aren't turning to him out of anyone carrying Ice Beam or a grass move who can ALSO take a hit from his STABed EQ, he gets trap damage and possibly a KO.
-Weavile also sucks for being U-turned into, and the Focus Sash variant slaughters you if you didn't start with U-Turn.
I'm not sure I know what you mean here. If you mean Weavile is too fragile to switch in, he isn't, and he counters a lot of stuff that walls this set. If you mean facing opposing Weaviles, coming in on SR or Sandstorm means it is OHKOed and if there's no support, it's just Weavile at 1 HP, all you need is a Pokemon that can take 1 hit and hit back with 1 move.
I mean, you've given us a Adamant CBer that you refuse to call a sweeper. Why should I use this instead of Ambipom which gets STAB on Return and the same speed, or Staraptor which is slower but also gets STAB Return, a second STAB, Close Combat instead of LOL Iron Tail, and has Intimidate so it isn't Pursuit bait?
The only thing Azelf has over any of these is Explosion. So Azelf is cool if you want a nuke, but otherwise I feel this is an underutilization of Azelfs potential.
My recommendation is to put either Grass Knot or Flamethrower over Paypack/ Iron Tail. At least that way you don't get horribly, horribly walled by Hippowdon or Metagross of all things.
Ambipom is too fragile if he has Life Orb, and does not have the same level of power without it. Staraptor is slower, SR weak, and is walled just as much by anyone who resists his STABs.
Grass Knot is a good choice. I emphasize that if you are worried by a particular Pokemon, Azelf has the specials to cover that.
Your damage calcs section doesn't really give anything useful. Half of those pokes already get annihilated by normal Azelf, Blissey isn't going to stay around and wait for you to 3HKO when you start unloading CB'd Returns, and things like Salamence and Garchomp take about the same damage from LO'd Psychics so.. what really is the point?
If you want I can add more calcs. If you notice I mentioned you won't stay in against Blissey, and if Azelf stays in on the dragons he's going to be KOed.
And I really don't like U-turn on Azelf. It's hard enough to get Azelf in to begin with without forcing him to switch out every time you do.
He isn't really as hard as you think to switch in, you can come in on most non boosted walls, depending on the set of course. With Grass Knot you can beat Hippo 65.71% - 77.14% with Grass Knot with ZERO Special Attack EVs. Skarm takes 67.07% - 78.74% from Flamethrower, again zero Special Attack EVs. Pick your poison.
This is horrible. Who cares what U-Turn does to Tyranitar? Grass Knot slaughters it. You already 2HKO Blissey with Stealth Rock + Sandstorm. You are dealing pathetic damage to everything by your calculations, much less than a special Azelf. The only thing that you hurt more with this than with some sort of special Azelf is Houndoom. And who cares about Houndoom?
By that logic I might as well use Specsmence/Weavile/Cressy/Blissey/Poryz/Infernape, and we can have all teams the same.
That said, a U-Turn from CB Azelf to Weavile brings a lot of things that aren't quite in Vile's KO range down enough for Weavile to deal with them. So they make a pretty nice combination for cleaning up. Assuming of course, that Vile isn't going to get hurt on the switch. This can be done to most special walls out there. They sure as heck are not going to be OHKOing Weavile.
Cresselia, Blissey, Sand Cradily, and maybe Regice come to mind
This is the idea. Doing appreciable damage to almost everything, then switching to a strong Pokemon who can KO the weakened opponent.