Wait, are you saying that Twitch isn't stealth based? lol?
Shaco's stealth is as critical to his play as it is to Evelynn and Twitch's, only his is not a "roaming" stealth. He can't activate it and then roam the map in search of an easy target. Instead, his stealth is to be activated just outside of the enemy's field of view when making the first move, and then again when chasing the enemy down. Shaco is possibly the most difficult hero to get away from atm. His stealth is a very important ability in his play, and it should be used religiously, just as with the other stealthers.
"Also remake Eve and never make the mistake of stealth-based again and we'll all be very happy. Thanks"
I would not be happy at all.
However, although I absolutely do not want Eve to be remade (she is one of my favorite champs), there should be no more made like her and Twitch. Shaco's style is fine because his stealth is limited, but adding any more hardcore, "roaming" stealth killers would lead to nasty gank groups.