Why does the new Eve's stealth only activate at 6+?

She needed the stealth because she had no gap closer. Now she has a gap closer so pre-6 if she had stealth and a gap closer it maybe a bit much. Once you are 6 you get your stealth back so you can choose to power farm till 6 if you like!

Part of why eve being picked was that everyone in the game had to change the way they play because they had no idea where she was. She had enormous pressure just because of who she was. That's not fair to have influence on every lane so early. You also shouldn't be forced to buy an early sight ward when gold is so scarce.

so she had bad clears and is invade-able

it's so that you aren't constantly warding to keep track of her, basically less oppressive early.

Because she would walk out of botlane with a double kill 2 minutes into every game otherwise?

So that the enemy can actually play the game before their first recall when they have no pinks

No early game cheese im guessing

The main reason she was so high up for a rework, besides her visuals, was because when she was strong she would absolutely decimate the early game since her ganks were very hard to escape from since you couldn't see her coming with a pink, which was typically unavailable before a first back. Riot allowed her to keep her permastealth, but removed it from the only part of the game when it was actually problematic for her to have and forced her to be underwhelming (unless fed) in other parts of her kit.

Shaco had the same thing done to him in the Assassin update by making his early ganks bearable without needing to buy a pink when the game started.

with the rework her early game is still good but if she still had stelth then that would be to much power with her old kit perma stelth was pretty much always needed