Magic Damage and Turrets

Because thats how its designed.

Kayle should get the same treatment. Otherwise it takes her 30 minutes to knock down a tower.

Why does Diana's passive proc on turrets and do magic damage, but Kayle's E magic damage doesn't?

The pattern I've generally noticed with stuff like that is this:

If you're melee DPS and don't stack tons of AD, then you're AA modifyers get to damage towers.

If you're ranged: you don't.

Also with Kayle it's worth noting:

tower/inhibitor/nexus damage is 100% of your Base AD + the higher of 40% of your total AP or 100% of your bonus AD. Towers are also flat-out immune to critical hits along with all forms of armor penetration and magic penetration: so AS + AD OR AP are the only stats that really do anything against towers.

AP is about half the price of AD and available in 120 chunks compared to 80 chunks with major items: or 156 compared to 80 with bonus. With a party-hat, AP is at 97.5% of AD's vs. tower potency.

AP+AS champions like Kayle are capable of killing a tower as fast as several marksman (if not occasionally faster).

Kayle doesn't have any issues taking down towers and doesn't need the help against them.

As a melee: Diana usually does have a few issues just as 125 is clearly worse than 525 range.

diana is too good to be true and kayle aside of not proccing E on turrets ,got base dmg - 5 ,so 51 to 99 ad is very very low for auto attacker

Kayle E is on on hit effect and attack range steroid. Diana passive is an empowered auto attack.

Its the same reason that Lich Bane damages towers, but Nashors doesn't.