As someone that has bought and tried to play him any which way from Sunday I will tell you that he is supremely outmatched as an assassin in every way against every assassin I've come up against... every single one. Don't get me started on mages...
His Q is slow, has an insane CD at early levels and is VERY easy to dodge. Even though it is a casting magic it is blocked as though it is a physical attack; thusly it is countered often.
His W takes about 5 seconds before cast and stun. Even slowed enemies get out of it... then its Ekko for dinner. Side note: It does not stun Heimers turrets.
His E is rarely effective as a dodge or an initiator unless I'm already up close / away from the enemy to begin with / KS ing the ADC - the only way he scores kills.
His R is rarely used to actually try to kill his opponent due to the fact that the combo of QWE takes about 10 full seconds to get off. Thus I'm almost always using it as a way to escape rather than damage an opponent. Even when I get close to an opponent the AOE is only RIGHT next to him. If I time my ult wrong and hes one full champ size outside of me (the center) it will not damage my opponent and I am killed.
The only way I can guarantee a kill is if it is a ks against another opponent. I've built him to be a mid assassin and get outlaned by just about every other champ I've come against. It was so bad that I gave up on mid (which is what he was supposed to do) and decided to play a Jungle Ekko with marginal results (lucky to get a 1/1 KDR). Feel free to look at my match history. I have been playing since season 1 so it is not a noob issue either.
If you actually want to assassinate the opponent, he is literally the worst assassin in the game.
He can't lane and he can barely jungle - so he's constantly gold hungry early game.
If you're lucky enough to survive to late game - that's very rare - it is impossible to set up a combo for a kill and you always die even if you spam the ult.
For an assassin there is no reward and plenty of risk.
Here's a link from the pros to give you an idea of how he fares with win rates, etc: http://champion.gg/champion/Ekko/Middle