Ezreal can definitely win lane (even against Cait) if played correctly. However you NEVER want to be shoved into your tower as ezreal. I know you've probably heard "focus on farming" but think about this: if you only focus on farming and give the other laner no pressure - they will also just farm it up. As well as getting damage on your tower and having COMPLETE control of the lane (they back when they please, they invade your JG as they please, they roam as they please).
Its not that big in maybe lower level play but being shoved in and just sitting there waiting for last hits is never a good tactic (even if you reach the juicy 10 cs/min - its just not worth it, thats why you will see pros occasionally give up last hits for lane dominance - because being able to ZONE people off last-hits and XP later on is much more worthwhile than last-hits right now)
Also remember - mid/late game rotations to make sure minions aren't being dissolved by other minions or towers is HOW you get a good CS score - not just last hitting. You don't get those high CS counts just cause you can last hit better, its because you can make the proper rotations to get all the farm on the map and still be in a position to pressure objectives.