Crescent Strike doesn't send her careening at the enemy with the same ability slot being pressed again. She has to burn more mana, and her ultimate, in order to do so.
I'd like to think that Pale Cascade is actually a superior form of Safeguard, given that Diana spends a bit longer in the middle of an enemy team at one time due to her lack of escapes. It also provides some healthy AoE damage that scales really well.
Not even a little. Cripple is a debuff that also deals mass AoE magic damage. Diana's moonfall stops her movement, knocks enemies up and slows them a bit, but adds nothing to her damage output.
Your comparisons are honestly just awful. Diana isn't a watered down version of Lee Sin, she's someone who's designed to be mobile enough to get in and go hard, not to get in, get a few hits, and then ward jump back to safety. You really don't seem to understand Diana's kit very well. I personally love her, she's quickly become one of my favorite junglers since two or three early points in her W lets her stay in the jungle for a LONG time, and I go incredibly ham with her through the mid and late games, as opposed to a Lee Sin who starts falling off in the mid and is reduced to a gap closing tank during the end game.
Diana's just fine where she is.