Wave Clear, Homogeneity, Philosophy, and you. Maybe an AP Hydra wouldn't be the worst idea.

Recently a thread floated to the top of Reddit that talked about Lux's problems with wave clear (E costs 130 mana by level 9 and doesn't do enough damage to one-shot the caster line without a significant AP investment or being really ahead). There are a lot of champions that "suffer" from this. A common response in the thread was that Lux is okay and that a few meta shifts might even bring her back into the spotlight again.

Even though I disagree about that specific point with regards to Lux herself, there are cases where this is pretty true. An example: Viktor isn't a great pick at the moment IMO but he's a strong champion and could easily see play if some of the more popular champions and comps were to shift around a bit.

The place where this becomes less true is with regards to wave clear. Wave clear is, like jungle clear, a PvE element. I don't think very many mages take advantage of an "increased damage to minions" mechanic (save for Ziggs' ult), so that means their raw damage output vs. champions (in lane trades in this case) directly relates to their ability to clear waves of minions. If you reduce a champion's wave clear you tend to also reduce their trading capability and mid-game skirmish power. Since mages tend to be mid-game focused champions to begin with (some do have a stronger early or late game, but almost all of them are most potent mid-game), wave clear appears naturally as an eventuality of mages just having AoE damage and needing to do damage to Dudes.

So the only way a champion with poor wave clear will ever become more desirable is if other champions also have less damage without their ultimates overall (because normally and especially in the case of Lux, a lot of their damage is loaded into ultimates). But is wave clear a problem? If so, when is it a problem? If wave clear is something that is sort of required for a champion to be desirable, then why doesn't every mage get to have it? I don't think it's a question of homogenization; aoe damage and thus wave clear is a feature of the class... mages having wave clear isn't anymore of an offense than all AD carries hitting hard with auto attacks.

I thought about this and have come to the conclusion that Riot might be flip-flopping internally on this subject a bit. Wave clear is a big enough thing that if your champion doesn't have it, they aren't often played despite all of their other strengths (see: AP Ezreal), but a champion might be balanced around a certain ability costing X amount and providing X benefits. Sure, Lucent Singularity is expensive and the damage to minions isn't that great, but it also back loads a bunch of damage into her ultimate, provides vision, and oppressive lane harass.

So, TL;DR:

What are the benefits and and disadvantages of the existence of wave clear item, similar to Hydra, for AP champions that don't have the greatest wave clear naturally?

No idea what this might look like... after using an ability, your next basic attack does magic damage to minions in an area around the minion targeted by the attack... something like that.