A Friendly Question about Bruisers :)

Hello there! Before I start, I'm not entirely sure about where this should be... it's more a question about gameplay design than a question about the state of the game. Sorry if I got the category wrong :(

So, my question: Why do most bruisers (that I can think of) have attack speed steroids/increases in their kits? Champs like Warwick, Vi, Kled, Wukong, Fiora, Xin, Olaf, Camille, Jax, etc..

Even off-bruisers like Diana

I understand they're damaging dealing characters, and attack speed increases boost their damage output. But I was just wondering, why mostly attack speed boosts? Why not attack damage boosts, penetration, other methods of boosting damage?

Is there a certain game design reason for why most bruisers get AS boosts built in?

Thank you for reading! Sorry if there's something obvious I'm missing...