Here's how it works -
Bane of the Stricken has in Internal CoolDown, which means that the proc ability from BotS does not apply with every hit, it applies when the hit and the ICD align to allow a proc.
So if your attack speed is hyper fast, the ICD of BotS will not match your attacks, meaning that you can hit 3 times in 1 second, not all 3 hits will apply the BotS proc.
It turns out that BotS ICD is snapshotted whenever you enter a zone, use a health potion, or revive.
Also, what this means is that the higher your attack speed is, the faster the ICD will expire.
In turn, most things that raise your attack speed while you are fighting, will not go towards the ICD of BotS, that is, until you use a health potion, in which case BotS will re-snapshot it's ICD based on your current attack speed.
Read this guide for more in-depth explanation.