Can we increase ezreals movement speed?

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I think there should be an Old Irelia style passive on him that while 1 enemy is near him each second, 2 seconds are removed from his E cooldown, 2 enemies remove 5 seconds are removed per second from his E cooldown, and if 3 are ever near him, he gains 50% damage reduction and 25% omnivamp and his E is instantly refunded in cooldown every second.

This will allow skilled Ezreal players to dance around the battle whilst allowing others to punish him for being so close. Also since he'll be in such danger, he needs beefier stats like a melee champion to compensate.

I think they should make it so if you proc W with E, arcane shift cooldown is refunded but Q does not lower the cooldown of shift anymore