Lets analyze your statement then, shall we?
Here is Annie:
http://na.op.gg/champion/annie/statistics/mid
skill order: Q > W > E.
Which means lv 2 to 8 you will often have lv 1 W.
And in the case you take a second W skill at lv 4, you will have lv 4 to 10 with lv 2 W.
Which is: 70 or 115 + 85% AP
Assuming you get according to you, Lost Chapter.
That's 25 AP.
So, lets assume rank 2 W and 25 AP. Your W will do about 150 damage.
Even a full
gives 100 ap.
Meaning, your W will do around 220 damage.
Do any minions have 220 hp?
Even if you add
that's around 350 damage. Still not enough.
Minions get stronger with game time passed. And here's the minion stats at lv1:
296 hp for casters
473 hp for melee
828 for cannon minion
491 for melee
302 for casters
851 for cannon
in the second spawn of minions
314 casters
528 melee
898 cannon
I went in a practice mode and went to lv6, added 10000 gold to my inventory and maxed W first (lv 3 by lv 6) and went back and bought a morello.
My W will do: 160+116 damage
Lv 4 was needed in W to be able to 1 shot caster minions.
Damage: 205+117
At the moment when casters had 320 hp.
And ofc, 6 seconds (6.4s actually) was the CD on W with morello on.
Now bro, can you still think you got wave clear on annie?
You can't even clear minions fast even if you max W until you get like lv4 in it. Which in pretty much all annie games. And that's lv 12.
So, aside the fact that you need 2 rotations to kill melee champions (and that's 12 seconds if you max W instead of Q). Which pretty much nobody does.
And this is not all.
You got the big problem of: W range which is sadly just 600 and very narrow.
This means you need to be in melee range of melee minions to be able to hit most of them. And this is in no way shape or form safe.
I also did another experiment. I went annie in the practice game, bought boots 2, ludens and morello.
Then I stayed in exp range to get levels of minions to get around when annie could get lv 8 very fast. And that's 8 minute mark.
A W used then was able to 1 shot caster minions with the ludens's extra bounce damage (And only because of that).
So, you still going to need most likely in a normal game. 1 W and 6 Qs to clear a wave without caster minions.
And that's with you being in melee range of the melee minions for the W (its not like Q has bigger range).
Which all in all means:
Annie has bad wave clear and meh wave push.
Also, since assassins are supposed to not be able to play against annie.
Here's an assassin vs an annie.
https://www.youtube.com/watch?v=l7zczePA9Jc
To be fair, the katarina main is on a smurf and knows his damage and the annie is just plat. But the point is: annie is squishy and has no wave clear. Assassins can kill her or simply roam.