I try not to pull the "As an X main" but Ezreal has a soft spot for me. I've been playing him since his release and I've watched every buff and nerf with bated breath. So, as an Ezreal main...
...I think its a testament to Ezreal's (other) strengths that even having 0 CC of any kind, and having 1 (basically) useless spell, he's still as good a Champ as he is. That said the distribution of his power budget is pretty skewed, and he suffers from a major identity crisis. Is he AD or AP? He can be either one, really, but never shines very well if he tries to do both. If he's AD, he suffers from an inefficient Essence Flux (not 100% useless since yes, he can buff himself and it does add a little damage) and his AP scalings are underutilized (although since he builds TF he at least uses it, a little). If he's AP, his passive becomes useless, and his AD scaling are then under-utilized. And Essence Flux, which is his best early game AP tool (wide, fairly long, goes through minions, great AP ratio) will tax his mana pool heavily, perhaps too much for it to be a particularly strong route to go.
Even within AD Ezreal only, he still has a little bit of a crisis. He's not a standard AA-based rADC, because Ezreal doesn't scale as well with crits. He's not meant to be a close range 1v1 duelist like Vayne, rather he's meant to kite, poke, harass, and snipe from afar. They took away his enemy AS debuff which was one of this best tools against the enemy ADC. Yet his passive still pushes him to want to AA and duel, since the stacks are temporary and directly buff his close range game. And since his Q, his main kiting tool, doesn't crit he doesn't have the same power curve and even role as your late game hyper carries.
Ezreal could be in Ashe's camp as a "Support-Carry" if they gave some better utility back to his W to make it more appealing. An AS buff is great for taking down towers but since you're usually the dominant AD on the team, you're the only one that really wants the buff. But again, he also doesn't like being in that close of range.
To further complicate things, Ezreal used to be considered the pentagon of "high mobility, ranged AD", but he's not really high mobility by today's standards. He has one mobility ability and 0 CC. Admittedly, as mobility options go, Arcane Gate is a great one.
Instead, I'd rather see his passive be changed to something like a stacking Movespeed boost, instead of Attack Speed, since it would further complement his mobile, snipey, harassing gameplay and focus more on his kiting. His Essence Flux could do something similar; give allies an MS boost instead of an AS boost, and slow enemies. Changing these two abilities to focus on his kiting and speed, while not giving him an oppressive amount of mobility and put him more comfortably into the zone of "Support-Carry", which was his original design (back when Essence Flux also had a HEAL), while also making his entire play pattern more cohesive.