Ways to make AP Ezreal actually viable
So, now that the last few remaining competitive games on patch 5.13 (the final patch of Runeglaive Ezreal) have been played, I have some thoughts on how to make AP Ezreal a healthy, exciting champion. Part of the trick in balancing Ez is making changes to his numbers that neither overly nerf or buff his AP or AD build. What the Runeglaive did for AP Ezreal was give him waveclear (which has always been what precluded him from being a viable mid laner) and also converted the full damage of a Q or AA + Runeglaive proc into magic damage. Without the item, AP Ez is back in an awkward spot where he doesn't have the waveclear of a competitive mid lane champ.
Here's my proposition: allow Ezreal's W to damage minions and monsters, but to balance for the AD build, make it so that his W only procs his passive against enemy champions. You could also reduce the ratio on the spell from 0.8 to 0.7 (Ezreal's ridiculously high AP ratios are part of the reason why he felt so toxic). This would give AP Ezreal viable waveclear, but wouldn't be broken because he would have to stand pretty close to the minion wave to W the full wave (allowing for plenty of counterplay in lane and in seige situations). The buff would also be a nice minor buff for AD Ezreal, as it would give him a small amount of lane pushing ability (especially with the early power spike of a Sheen), and would give him just the boost he needs to not be garbage in lane (which he basically is currently).
Secondly, I think his ult numbers should be changed. One of the most absolutely frustrating things about a viable AP Ezreal is the prospect of him hitting you with his ridiculously high scaling ult - a whopping 0.9 AP Ratio on Trueshot Barrage basically allows him to (from anywhere on the map) chunk people to hell and back when they group for objectives. Here's my proposition for his ult - reduce the AP ratio to 0.7, but ALSO reduce the damage reduction it suffers the more enemies it hits from -10% damage per enemy hit to -5% dmg, and instead of the damage ramping down to a minimum of 30% damage, cap the damage reduction to 40%. That would seriously smooth out the power of his ult, and make it much healthier for the game.
Other than that, I think everything about AP Ez functions quite well. Mystic Shot can't apply spell effects, so he doesn't have a broken amount of synergy with Rylai's or Luden's. Ez' Q is overall healthier in the AP build without Runeglaive, because now he can't convert all the damage into pure magic damage; this makes it still a very good delivery system for Sheen items (Lich Bane and sometimes IBG being the common choices for AP Ez), without being a completely broken poke tool. A Lich Bane empowered Mystic Shot in an AP build would functionally be half physical damage, half magic damage, so it makes his Q much less effective against tanks, and even does reduced damage to squishy champs because of natural armor growth. His E damage is pretty high scaling, but also rewards risky all in plays, so I think the current 0.75 AP ratio is fine (it could maybe be tuned down to 0.7 or 0.6 and still be strong but not broken).
I personally really like AP Ezreal, I've always loved this Champion's theme, design, and gameplay, I just would like it to be in a strong but healthy state. With the current state of the game, there are so many champions that have mobility, waveclear, high damage, CC, and innate tankiness, that I don't think it would be unreasonable for a mobile champ like Ezreal to have viable waveclear, and balanced damage numbers.