You are right. Magnus Carlsen was born with a 2800+ rating.
He had rapid improvement - which I explained in my post if you read it.
I'm asking for an example where it's SLOW and steady improvement over a long period of time
Carlsen's improvement is a slow and steady improvement over a long period of time.
2 and a half years ago I was stuck in mid 1500s blitz. Right now I am at low 1800s - high 1700s blitz on this website. That's a 250 points improvement in the last 2 and a half years. According to OP I should have been forever stuck on 1500 blitz rating and yet as of the moment of writing this comment I am rated 1826 blitz.