the issue with ezreal support is that you have skills shots that provide damage only in your kit.
for example your Q is physical and counts as a basic attack. this can be easily countered with tabi.
your E is magical and is your only escape tool. it requires you to sit on it so you dont die.
your W is a champion only close range skill shot that can only slightly boost the attack speed of allies. it doesnt heal or shield so you cant combine it with any items like you could by using censor or redemption. and the range puts you in proximity of enemies that are likely to 1-3 shot you.
and your R is a wave clearing wide shot global that's only purpose is to last hit fleeing enemies.
since you're not going to be building damage it wont be able to do the job it's meant to do.
not to mention your kit will in general be weaker overall.
and then you have to think about an income item. the only income item that would be beneficial to ezreal is edge since you could use w to harass champs from behind the minion wave. however that puts you in range of most marksmen and mage champs. not to mention your mana costs are high and the cooldown of your spells relies on your auto attacking.