Shaco's blink is a very good tool, but it only serves either a gapcloser or as an escape as it has a long cooldown, and while his ult CAN be used defensively (it has an invulnerability frame), its hardly an escape, best case scenario he can use it along with his boxes to stall long enough so his Q comes back online, but that is FAR from a free escape.
Ekko's ult while probabably being an even better escape than Eve's ult does make you CHOOSE between escaping or trying to damage the oponent, aditionally while an AOE stun does sound more powerfull than a single target charm, ekko's W is a lot more telegraphed, delayed and harder to apply, like it or not ekko requires a lot more PLANNING AHEAD to be played at full potencial.
As for zed and leblanc, just like evelynn they also have way to get in and out of battle and guess what, their escape is ALSO a blink, just like evelynn!! Their escape blink however DOESN'T come with free untargetability... which means that a in a clutch 1v1 if both targets are low, they actually RISK dying, unlike eve.
Against Zoe you can fight back just like a zed or a LB as her ult doesnt grant her an untargetable escape. Sure she has a lot of other issues, but I dont actually have a sugestion on how to easily make her kit healthier without ruining the champ, its the entire concept of her kit that makes her somewhat problematic atm.
Anyways now that I've adressed the champs individually, you might notice a pattern here... every single champ listed has to MAKE A CHOICE (shaco either engages with q or disengages with it, ekko either uses ult to escape or to burst; and as for zed, lb and zoe while having an engage and disengage they ALLOW you to FIGHT BACK). Evelynn just DOESN'T have to choose, she has the best of both worlds, her ult bursts, disengages and prevents fighting back, which is the point of all this, removing the untargetable frame wouldn't make eve useless at all, it would just bring her closer to the remaining assassin's level.
Lastly, regarding Rengar, I have NO IDEIA if he is going to be back to being "broken" but I really hope so, I'm looking forward to his next changes