Attack Speed Functionality

I've been browsing this subreddit, and I've come across a lot of people saying that a higher base attack speed helps a champion's scaling with attack speed items. I may be wrong, but my understanding of attack speed items is that they are an additive multiplier, meaning the sum of the percentage increase in attack speed you get from leveling up, items, runes, masteries etc. is multiplied by the base attack speed.

Hypothetically, when two champions have identical DPS is spread differently between their base attack speed and base damage, wouldn't a percent increase in attack speed have the same DPS increase for both champions? Essentially, attack speed is simply a multiplier of DPS.

The only thing I think base attack speed would effect is your damage. Your attack damage is worth less if you have lower attack speed since attack damage is a flat increase, not a percentage increase.

Thoughts?