"Dont let her run on top of you to ult" Right. Because your typical mage build does not provide a ton of movement speed. Neeko does not have anything in her kit that can let her approach slower enemies. Her primary counterplay is "dont get into her very long basic attack range, ever". You don't see the problem here?
Her skillshots have very wide hit boxes, and even if she misses she has a lot of movement speed compared to many older champions. Her ultimate slows, shields her and then stuns anyone inside its range - and its range is actually greater than an Amumu ult.
So basically, you NEED a mobility spell, an extremely high cooldown summoner spell or a very specific situational mage item to dodge her ult. When Neeko's ult has a 90 sec cooldown at level 6, BEFORE you factor in cooldown reduction.
You really can't see how overtuned she is? Compare her to champions with similar abilities - Nunu, Ryze, Wukong.