After looking at a lot of the empowered autos in the game theres so much inconsistency. Nasus q can hit towers so why can't yoricks? Aatox's w cant hit a tower but xins passive can seriously what puts the line of can and can't hit a structure. I mean some do make sense like jax's empowered autos not hitting because that would be retarded but other autos really feel like they should effect structures.
Consistency and Riot go together like ice cream and cabbage.
it's for balance reasons
remember when birbman 
could use his W on turrets which made him better at pushing turrets than any utility mage?
and then they got rid of it because he had too many strengths. because of balance purposes.
Yorick so he doesn't take 2 turrets in 20 seconds and Aatrox so he doesn't heal and 1v1 turrets.
The real question should be why isn't it mentioned anywhere in each of their ability descriptions
you answer your own question in your post.
I mean some do make sense like jax's empowered autos not hitting because that would be retarded
so you already understand that it's used to help with the balance of a champion. case closed
It's champion specific, depending on how much power Riot wants to budget into tower-killing on a given champion and how much access a given champion tends to have to unattended towers.
Idk i don't see how it's okay for nasus to hit towers and jax can't. I mean we've all been there when Nasus literally take 2 towers in 30 seconds because my team chose to fight a 5v4 that ended well, but 30 seconds go by and our inhib is gone. How is this healthy?
In practice, empowered autos are prevented from damaging turrets when Riot doesn't want the champion to be good at splitpushing. I agree that this is terribly inconsistent, and that if a champion is innately good at splitpushing, or too good at it, then that needs to be solved through gameplay changes that target the actual playstyle more consistently, not special-casing that is damaging to clarity.
What also frustrates me is that often this kind of exemption is given specifically to fighters, a DPS class that should by all rights have good pushing power, whereas marksmen, who almost all have some sort of autoattack steroid, are fully allowed to convert their own abilities into turret damage, while also generally having no other limitations to their waveclear either. At the very same time, marksmen are still excused for being mandatory under the pretense that they're supposedly the only class capable of taking turrets down properly, which to me feels like even more of a double standard. More generally, I feel many more abilities, not just empowered autos, could damage turrets and still be fine, and I'd be in favor of increasing turret health in compensation for having them take damage from abilities, particularly since it could open up interesting opportunities for artillery mages and other casters.
It's all up to Riot on who can do it. I believe the reason Yorick can't is because of his ghouls already giving him enough split pushing power. It's the same reason Jax can't because of his already stupid strong split pushing.
Recently Trundle got his tower bite back after a year or 2 without it, so it's whoever Riot decides needs the ability to do it.
its balance,trundle was in a bad state and bramble vest was about to rek him even more so riot gave him a chance as a splitpusher by letting him use his q on turrets. yorick already has too many tools to push,if they did change his q to be used on turrets they would nerf everything else,be carefull what you wish for
They should just completely remove the ability to effect towers from all empowered autos abilities
They stated this before. It's a case by case basis rather than an all encompassing rule.
Should it be that way? Idk. That's just how it is.
I would love if they'd let Yorick Q structures though. For a splitpush champ it takes alot longer to kill a turret with your whole horde compared to Nasus just Q'ing it.
Its used as a balance tool. For example in patch 6.1 trundles ability to q turrets was taken away and re-added in patch 7.13.
they said it's usually a good thing to give champions power or take it away from them without affecting their gameplay too heavily.
for example when a champion is underperforming giving them that ability is a nice buff with low risk of making them end up broken.
