What if Last Whisper costed more gold, but in exchange a new item is in the build tree?

This is just a thought, but with how powerful Last Whisper is (pretty much invalidating armor) isn't it a little too cost efficient?

For 2300 Gold you can basically give a big middle finger to all Tanks and Bruisers for the entire rest of the match, along with dealing more damage to most people due to penetrating natural armor as well.

Whilst I admit I am a bit biased due to playing melee/tanky Champions, I feel that for the power spike it gives ADCs the item is far too gold efficient, and would like to recommend something to try and fix the situation a bit.

What if Last Whisper's price was increased (not drastically but still making it cost a hefty amount of gold), but in exchange there would be a new item in it's build tree with a weaker passive?

This new item would build from Long Sword and Pickaxe, and in turn would build into Last Whisper. This new item would have a weaker version of Last Whisper's passive, still giving ADCs the ability to fight Tanks and Bruisers, but not allowing them to pretty much invalidate said enemy's armor/defense as easily/early as they do due to Last Whisper's cheap price.

Do you think this would be a good (possibly short-term) solution to the issues regarding Last Whisper? Do you think its an unnecessary change?