I haven't been liking her much on the PBE either (with the buffs and new runes, but I'm still experimenting with runes tbf).
Your point about assassins is accurate, but the thing about assassins is they can still be useful at all stages of the game. Take zed for example, he's good early due to working on an energy mechanic which allows poking and trading while farming, mid game he has a global presence with his roam potential, and late game he has a split push global presence + target elimation.
For a jungle assassin; Kha'zix is powerful early, able to dish out tons of damage alone and in ganks, while having a relatively good clear. His objective control due to isolation (with drag and baron) is amazing, and his resets enable him to make smart plays on going in, picking somebody, and getting out or going for something else. Additionally he can take towers relatively easy being an AD assassin.
A non-assassin, but rather diver such as Elise, is an AP early game monster with strong diving potential, one shot burst potential, tower sieging due to attack speed on W and spiderlings, a healthy clear, and if all else fails, she can build more off-tank with fitting in tank items over AP if she's not consistently doing the damage. This is the one to compare to Evelynn because while Eve is an assassin, you have to ask why play eve as an AP assassin when Elise is an AP assassin half the game, but more consistently, with non-ultimate wasteful escapes, a better transition into the late game, and a plan B option.
New Evelynn's lack of versatility with a highly predictable kit and no major global presence due to wave clear issues is her biggest flaws compared to other assassins. The mid game powerspike and unreliance early game (all game) just add to her champion design, which in its own is terrible.
Even in the sentiment that "assassins are weak because ADCs/Supports are strong", eve would still be the bottom of the barrel compared to everything else.