Her long range lets her poke in lane. If she tries to walk up and auto attack people (or even Q them against some comps) she is putting herself at huge risk for little reward; she might outrange the auto attacks of the enemy, but CC? Gapclosers? Artillery?
Cait does use her ult to poke a bit before fights, but that is a rank 1 ult with 1 AD item backing it. It doesn't do very much damage unless the target is extremely far behind.
Caits mid game doesn't even come close to the others. None offer simultaneously as little damage and utility as a Cait in midgame.
Damage steroids on her passive and Q, massive utility on passive, E, and R, initiation on R.
Very high base damage on everything, and it's split damage so tanks haven't built against you yet.
A steroid on W and high base damage.
A steroid on his passive and W, a short CD escape, and some decent base damage.
Tank stats and some of the highest midgame burst in the game.
A steroid (kinda) with his passive, high base damages, and initiation on his W and R.
A steroid on her passive and Q, CC on her W and E, and decent base damages.
Turns her support into Malphite, is the most mobile champion bar none, can secure objectives while asleep, decent damage even with one item.
She has the utility of her ult and an assload of damage (if she won the early game).
High base damage, a steroid on his passive, high mobility.
Steroid on W and an ult that will kill anyone it touches.
High base damage, high map mobility, and some of the most annoying CC in the game.
Steroid on W and one of the best ults in the game.
Steroid on Q, high base damage, resetting mobility.
Steroids on Q and R, decent base damage, stealth.
High base damage, CC on W and R, initiation on R
High base damage, steroid on passive, CC on E and R, initiation on R.
Steroid on Q and R, CC on E, repositioning tool on Q.
AOE root, steroid on passive and W, a Fizz jump on R.
Meanwhile...
A "Steroid" on her passive, which does nothing until you have multiple AD items and doesn't happen often enough until you have multiple attack speed items, a Q that is dogshit outside of lane, Traps that can be seen and walked around. one mediocre escape on a very long CD, and an ult that is only really useful for last hitting a squishy.
If your game plan for mid game is "don't fight", then I've got bad news for you; Cait is the only ADC who wants to do this. Other AD's have a similar power dip, but all of them at least have something to keep them relevant. Cait has her traps, but those are made worthless by things like rotations, flanks, or having eyes.