This is why I take Statikk Shyv on Ezreal.
Damn son! Now it crits!
Bye bye rapid fire cannon.
Damn son! Now it crits!
Bye bye rapid fire cannon.
Oh wow so impressive... they made a static shyv crit a VERY long time ago.
You could have achieved the same with 
mystic shot has been able to critical since season 6 i think. the one benefit that statikk shiv gives is that it chains to 4 targets and those chains can go through minions. riot actually encourages players to buy both rapid fire canon and statikk shiv because it allows players to combo off of turrets.
I thought Ezreal's Q is coded as an auto? It's why it applies on-hit effects and buffs (like Nami's Blessing).