I did it and I now sleep better, need less sleep, feel more awake in the morning, and save money.
This is one of the best 'life hacks'
I have every expectation this differs dramatically person to person, and I encourage anyone with any sort of habit to examine it, but what you say does not necessarily apply to everyone.
I've sworn off caffeine twice in an effort to regulate my sleep better and neither time has it helped me in getting to sleep. What it does do is in the "morning" [ie when I wake] make me more alert, I'm not in caffeine withdrawal, I feel better.
If you're going to try it then my advice is to ensure you still drink enough: substitute caffeine drinks with water for example.
For me going cold-turkey it takes about 1 week for the severely painful headaches to stop and for me to be able to think clearly again.
So far as I can determine caffeine has potential long term positive effects, doesn't have lasting negative effects. I slip back in to it because it's in the house and at times I have to use something to wake me up when I'm sleep deprived. It's pathological.
Every time I start in on caffeine again because of a crunch I end up regretting it later.