No we don't. Public schools are incentivized not to help high performers. It actually hurts their metrics and budget. The widespread gifted/talented experience in public school ended in the late 90s.
The actual intelligence segregation is self-selected. PMC parents live together in the same neighborhoods. Whether you believe in genetic or social factors, the smart kids come from here.
In the 80s and 90s there was an educational culture that believed in finding overlooked geniuses regardless of where they are from. That narrative is completely dead. All institutions expect kids to come prepared with a resume from their youth, and have few avenues for identifying talent that doesn't meet their mold.
Seattle Public Schools currently still has a “Highly Capable Cohort” program, though it is phasing it out.
I don't know where you're getting that from. The sorting of students into "gifted" and "non-gifted" categories is very common. You don't need to look further than your local school district for proof.
Check out NYC school district. Has high schools where entrance is 100% based on a single entrance exam score.