For fun, mostly. That's damn fun, though still useful and working perfectly on aggresive enemy teams, due to his big escape potential and harass from afar. He bases everything on his Q, spamming it, making it deal tons of damage with a muramana and all the other big guys, and making it slow people AoE with the iceborn gauntlets. the high cooldown reduction, favored by his spamming Q, lets him escape from every situation.
So you should go Blue if the enemy team is particularly dangerous for the ADC, or your team needs control and poke etc.

PROS

Damage from afar

heavy escape potential

heavy control and good scaling lategame

fun to play

CONS

Not that good early game

Not the same damage as the standard ezreals

Bases all on skillshots

Last hit minions with basics, obviously, but also use your Q to simplify it, use it even more when buying the tear/manamune. you'll be able to engage for a fight when you have Sheen, if not, engage only when a gank comes or when the enemy is low.
Resuming, play def and farm!

Group up with your team to take dragon.
Manage to take bot turret, and maybe help to get mid turret.
This is the part where Ezreal gives his best, so be present in fights

The blue build gives you a good advantage in lategame, differently from the standard ezreal, you maybe aren't good as a Vayne or a Tristana, but with the muramana's active you become very dangerous! group with your team, fight from afar, and use your scrying orb to take sight on bushes and dangerous zones.

A lot of people think that the adc has to focus a mage, an assassin, or the other adc, but thats wrong.

THE ADC FOCUSES EVERYTHING THAT HE CAN DO IN SAFETY.

Never forget that.
Anyway, start teamfights with an early R to charge up your passive, the attack speed is awesome on muramana strikes, though dont be greedy for kills! you cant risk your life to take one.

Why these supports?

Because you're a burst damage adc, so all you need is an offensive support with snares, tanky or not. Sona differs from the others because of only one stun, but she also heals and gives shields, she's maybe the best for Ezreal, blue or not.