I think public schools are focused on raising test results- the kids who come into school reading and doing math may not be the priority.
My DH occasionally interviews for jobs out of state- as a result I have looked at the school districts in quite a few different states. It varies--the best public situations that I have seen are four tiered:
1. grade acceleration is not discounted as an option
2. there is subject acceleration for children needing a challenge in one broad area (reading or math).
3. full day gifted or separate gifted schools for highly gifted students.
I had the frustrations that you mentioned in a private schools with far fewer students in the class. I think teachers see what they expect to see. When my DS began daydreaming and becoming careless in his work, his teacher immediately assumed he was having difficulty understanding the materials.
After simmering down, and changing the school situation, I realize it's because comprehension issues are what she sees 99% of the time in these situations.
In short, it would be great if teachers asked questions about milestones, abilities, interests and personalities at the beginning (although my DS behaves differently at school than he does at home). Our school actually did ask these questions, but the information didn't get transmitted year-to-year, making it ineffective when the "academic" curriculum started in earnest in the first grade.
