There's a thing in League called "Wasted passive" Which means if you buy two of the same item you lose a passive slot that could have been filled with something else which is why you don't get sunfire cape and cinderhulk at the same time.
Lich Bane is something a lot of on-hit mages use like Fizz or sometimes even Zigg's does it for some reason.
Personally I use it on my
And one thing I don't want is this item changing. More attack speed means wasted stats and CD means I don't get the damage off I want to get off. Basically it means one of the best items on Sona is now a half wasted one sure its benefit is still there but something else could take its place some other item that I would benefit from all stats not just 2-3 and have 2-3 wasted ones.
I'm not sure what you had in mind but these items do not need to be changed. Especially on champions like Azir or Sona it would really throw off their build path and possibly make both items more useless then when they're separated.
What I'm hearing from you is "I want an extra item slot" - and not - "I think this would be a quality of life change"