How come an Ezreal is always the one who does the most damage in a game?

he's not

Poke champions usually have a lot of damage dealt.

Q poke. He won't do any dmg without a strong frontline that can tank and dive.

he usually has the most deaths in my games

Poke champs generally have the highest damage

Depends on the team comp. If he has a team that can enable him to dish out constant damage he will. As will any capable ADC. It's kind of what they do.

1. Poke damage
2. 2 AOE skills
3. He's an adc with decent range