"A child who is already significantly ahead is so because they learn faster. The attainment gap naturally widens with increasing age unless they are artificially impeded in their development.
Most kids learn to read adequately, so the difference between a kid who was reading fluently at 3 and their peers who were not at 6 is no longer so visible to a casual observer at 10, but there will be enormous latent differences in cognition. It doesn't level out."
This only works if we assume that all gifted children have the same interest to learn to read at 3 and that learning to read is the only way in which they can stimulate their giftedness. Which may be rather a large assumption.
I taught myself before I started school, having got the grown-ups to explain the sounds of the alphabet. My db did not learn to read until he was taught at school. By the time we got to secondary, having both had every opportunity, he was ahead of me. He knew as many MFL as I did but also played an instrument to conservatoire standard and got top marks in STEM subjects.
If your theory held true, the attainment gap between us should be in my favour. It isn't.
I suspect the reason for his slightly later approach to reading was precisely because he was such an all-rounder: he was busy learning carpentry and sports and music and didn't need to read to make life interesting. My talents, and consequently my interests, were always more narrow, and being more of a dreamer, I had a need of ready access to stories.