Why isn't there a Recurve+BFS item?
This seems like it should be a thing.
This seems like it should be a thing.
Attack Speed is a complement to raw AD or on-hit effects. Getting decent AS on an item that also provides a large amount of AD would defeat that purpose.
Note how currently no item that grants both AD and AS grants more than 30 AD.

[{quoted}](name=Naut A Liss,realm=NA,application-id=3ErqAdtq,discussion-id=O1FcThlT,comment-id=0000,timestamp=2015-07-10T22:05:38.899+0000)
Attack Speed is a complement to raw AD or on-hit effects. Getting decent AS on an item that also provides a large amount of AD would defeat that purpose.
Note how currently no item that grants both AD and AS grants more than 30 AD.
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Maybe someone wants to sacrifice raw point and click power by forgoing Crit and running AD/IAS to improve their AD scaling skills and/or their tower pushing? Just maybe?
Once a champion has more than 120 or so attack damage, Crit chance is a more cost-effective source of DPS. An AD/IAS BF sword item would, thus, need to be focusing on something other than raw DPS since competing directly with IE/Dancer just isn't going to cut it. BF/Recurve would obviously get some kind of OnHit effect, something that wouldn't interact with Crit Chance.
So the question is, what kind of OnHit effect could interact with Bonus Attack Damage in an interesting way? Stacking bleed? Bonus damage to objectives? Stealing flat armor? A stacking debuff that empowers your next spell against the target somehow? Lots of options.