We don't necessarily need drastic changes to AP items, we just need more of them
Right now there is a large lack of item diversity for mages and the issue isn't that some items are overpowered or under-powered, it's that there is a lack of AP items that fulfill desired, more broad niches. Playing vs. a lot of AD?
, vs. AP?
, want to burst squishies?
, Need help vs tanks?
, mana problem early game?
, mana problems lasting to late game?
, nothing else to buy and need a lot more damage?
, better poke?
, AP scaling basic attack style ability?
, keep enemy at mid-range?
, diver?
, are you Azir? 
As can be seen, most of the niches only have ONE option to them making the decision in buying items linear, or some of these niches apply to very specific cases as with
and
.
Something could be done to the items to make those specific niches a little more broad, such as lowering the internal cooldown and damage of lichbane to make it more desired by those who weave auto's between spells, or make nashor's tooth work on towers to make it desired for tower taking and split pushing.
However, I'd like to just see more items get made out of components like
,
, and for
to get the
treatment, turn the item into a component item and the final items to fit different roles such as better vs. health stacking (same thing Giant Slayer does) or better vs MR stacking (black cleaver style but with MR). The examples I gave there shouldn't be taken too seriously it was just something off the top of my head, I recognize that an MR version of black cleaver could be busted completely.
Obviously, Uniquely named passives would be necessary to prevent people from stacking these niche items.
at least 1 item for ap assassins that is as strong as duskblade/counters shields

