Well this actually could work, but why the hell do you abandon lichbane?
Its simply awesome on almost any AP lategame, and on Ez its a nobrainer, you still use pretty fast auto attacks and Q works with it so you got nice dmg on your Q once you have lichs.

I also think AD Ez is more effective, but I still play AP cause its usually more fun having w/e for dmg, not only for utility and even Q deals nice dmg once you got lichsbane.
Add lichsbane for +1

Assists + mejai make up for lack of kills, and by the time u get voidstaff its normally gg. All his spells except mystic shot are "effective", I suggest trying the build before criticizing.

This was also not to be compared with AD build. It was a nuke AP build aka rely on ultimate to do the work mostly while cleaning up with flux and shift.

ehh. I'm not convinced this would work. The only time I feel like a build like this would work is if you somehow got several kills early game. The problem with AP ezreal is that he CAN be very good, but you need a TON of gold to give him awesome AP levels. The problem with him is that if you aren't the one on your team who get's that last hit to get the kill, you simply won't be powerful mid or late game.

I'm not convinced AP ez is viable simply because he only has his W as a reliable damaging spell which you can use repeatedly. And it still has a decently long CD.
I used to main as AP Ez, but recently have been playing him only AD, which I have found is far more effective.