Ideas for some AP items/adjustments

Looking back at the post from Repertoire a while back, just gonna post some ideas I got for AP items/adjustments to make them more diverse and interesting. This will be split into more general ideas (something that needs to be done but I simply don't have a solid idea as of yet) and then specific ideas (self explanatory).

General Ideas

1. Slightly nerf Morellonomicon and introduce more items that incorporate Lost Chapter. A big issue currently with mage itemization is that Morellonomicon is far too desirable for covering up mana-gating on mages while still providing a hefty amount of AP and CDR. Should a bit of AP be reduced from this item and distributed to other items it would allow the item to be more focused on mana sustain and less of a 1-item-wonder powerspike. Introducing more items that build out of Lost Chapter (the core item that assists in mana sustain for mages) would allow more diversity as well based on the type of mage being played. Could create a combination between Lost Chapter and Haunting Guise to utilize as another flat M-Pen item for burst mages early game.

2. Increase the power of what makes certain items unique in a trade off for higher gold-cost. are the biggest offenders I can think of at the moment. By increasing the power of the passives/actives of these types of items it will help express specific playstyles. Don't necessary increase the raw power of the items otherwise it will be toxic to opponents when the actives are there, but instead increase usefulness towards specific purposes. (Examples being remove the base AD scaling on lich bane and change to higher AP scaling, decrease internal cooldown of Sheen effect to allow for skill expression of auto-weaving in mages, have the slow on GLP stack when hitting multiple ice shards to better help with kiting, etc.).

3. Add in a LOT of new items meant to fill different niches. Right now some of the item types that are needed most are bruiser-style AP items, Assassin AP items, and DPS AP items. Currently all those different types of AP champions build solely AP items meant for burst mages which weaken their potential expression of intended playstyles. Obviously, many of the items will need Unique effects that won't be able to stack together to avoid abuse of certain combinations.

Specific Ideas

1. Make Nashor's Tooth a signature tower-taking AP item by making it work on towers. Lower ratio by small amount, but make do bonus damage to structures.

2. Change/Remove sorcerer's shoes - Having 15 Mpen tied to such a cheap item allows for early purchases and naturally ties down Mage power too hard to the early game. Boots of Lucidity could easily become a better staple-boot item for mages.

NOTE PC is about to die so will update this later today.