Doubling down on Ezreal's passive AS boost is not, IMO, the way to solve his problems.
I have spoken at length about my take on Ezreal before, but I'll try to summarize my thoughts. Ezreal's natural synergy with TriForce, combined with the fact that his Q (his primary source of long ranged damage) can't crit means that Ezreal just does not scale well with crit and, thus, does not scale well into the late game alongside other hard carries like Jinx.
All late game carries tend to either scale with Crits (because they rely on AAs) and often have some way to complement this, such as Ashe's unique Crit scaling, or huge AS steroids like Tristana and Jinx. The successful carries who don't scale with crits have some kind of alternate damage source, such as Vayne's Silver Bolts and Kalista's Rend stacks. Ezreal doesn't really fit in the Crit camp, yet he has this AS steroid passive which encourages him to get in AA range. However Ez's AA range is relatively small, he doesn't usually build a lot of crit, and he has one of the lowest base MS in the game. This combined with his 0 cc, all skillshot kit means that he just can't compete 1v1 with an equally fed enemy carry - Ez relies on kiting and range. So he'd fall into the "alternate damage" camp, except that Ezreal's damage just doesn't scale that hard.
He's caught between these two camps - either he goes into range and benefits from his passive, or he stays at a distance and kites. They don't work all that well together, and you combine that with his AP/AD hybrid scaling and he just sort of ends up a jumble of disjointed features.
Also, Ezreal used to be considered a "high mobility" carry, but with the amount of mobility in the game he is outclassed. He only has 1 mobility spell, and that is his entire safety/mobility budget.
Instead, I'd propose these changes:
Passive:
Change AS to MS
W:
Change it to better fit some kind of alternate damage source. I don't know exactly what it'd be, but I'd say something like: every X abilities that hit a target, Ezreal's next Basic Attack deals Y bonus damage. This would be similar to GP's passive in that it cannot be proc'd with his Q, but has to be with an AA. This would fit the whole "weaving AAs and spells", but doesn't commit him to the "boost your AS and go ham" strategy.
