The real problem with stealth is that it's inherently strong for the person using it. Riot's idea of counterplay is "How can we make this easy for the opponent to deal with" rather than, "Do players have the tools to deal with this champion's playstyle." Assassins are generally hit or miss because if they can delete you they lack counterplay and if they're like Zed they can get their entire burst eaten by a flash or a zhonyas. Problem is Zed still has his stupid amounts of AD and sustained damage so he's his own level of stupid.
Stealth has the tools to be dealt with, however League is a game that isn't built to handle stealth as is. Look at Dota2. Not only do they have pink wards they also have an item that you can hold and it gives you a huge detection radius for stealth. Because of this stealth heroes are allowed to exist because countering them is as easy as buying that gem. The counter to that, however, is your team working to take them down as the gem drops on death. It's very engaging and really rewards both sides for outplaying the opponent. League doesn't have that and adding it would be silly because the game simply isn't made in that way. That's why they have to implement mechanics like the alert on Rengar's stealth. I still believe that is a really silly idea because what's the point of stealth if you still know they're there. I don't care if I can't see Rengar as he's running up to me, if I know he's there I can play as if he's visible which completely defeats the purpose of stealth.
As it stands, Eve is honestly just a fighter with a really awkward, thrown together kit that's immune to green wards. She's not really an assassin because she has no burst, she's more sustained dps and an initiate ult which leaves her more like a bruiser than anything. Eve is definitely a character that can exist, perma-stealth and all, but they need to make her with that stealth in mind. Her theme is that of a stalking hunter, a crafty assassin preying on the weak. She should be someone that focuses entirely on picks, lacking meaningful ways to wave clear or teamfight in exchange for assassination power and her stealth allowing her to position well. Sure the argument of "Oh she'll just walk over to the ADC and kill them for free then die and that'll be a 1 for 1 that always benefits her team." and that's certainly a valid argument. However I think if we forced her to be similar to Kat where she thrives on cleanup she'd be much better and healthier for the game. If Eve has to stalk and pick weak targets and lacks many real ways to straight up duel or 100-0 people unless she's really ahead I think she'd be totally fine.
Not everything needs to be fun to play against, fun is obviously subjective, so focusing heavily on counterplay is something that's strange. Play a game of MTG in legacy. You'll tear your hair out vs something like stacks or death and taxes but those decks have counters and while they're a bore to play vs and grindy as hell the satisfaction of out playing the opponent is what everyone cares about, not sitting there giggling as death mark ticks down while you sit in your Zhonyas. That's like constantly holding a counterspell plus mana to make sure your opponent never can get a dude out instead of forcing your opponent to make meaningful choices about when and how he has to approach each turn. As long as there is some way to make sure a champ can't freely do exactly what they want, they're fine in my book. Mages have magic resist, assassins have Zhonyas/GA, ADCs have armor, true damage has HP, and stealth has true sight. There's no reason stealth can't exist except by Riot's own dislike for the mechanic or inability to give up their obsession with stacking the odds in the opponent's favor to make sure bronzies can process the idea that "well if I do this I can be that! Yaaaay"
simply can farm with 
. She still gives pressure on all lanes.
could make her more gank oriënted but it's not worth it while 
direction brings nothing to her lategame.