I think we need to rethink the entire system. Every student learns differently and at a different pace so forcing everyone into the exact same experience isn't going to work. Maybe there is a case for more advanced opportunities based on academic (or athletic, or any other criteria) achievement. I don't think that requires an entirely separate school.
You're absolutely right that every student is a unique individual. You want to teach students individually. One of the drawbacks of this is that the gifted will not reliably be positioned to raise up their less gifted peers, as divergence in individual instruction compounds over time.
I've seen schools that offer advanced opportunities based on academic or athletic criteria. In practice, they tend to look like gifted students in AP or IB courses and their less gifted peers in other courses. You don't need separate schools to get de facto segregation - all it takes is a series of advanced opportunities on offer.
With all this in mind, how do you propose to offer gifted students opportunities and material equal to their abilities while keeping them available and relevant to help raise up their less gifted classmates?
Like I said, I don't know how it would work but I don't think segregated schools are the solution, that's a step too far that eliminates opportunities for students of differing academic achievement to find common ground and teach each other something.
All students should be challenged up to their potential, having two options isn't fine grained enough. What do you do about the kids that are bored even in the "gifted" programs?
The best known solution that I'm familiar with is to allow independent study work. Larger schools also allow for more coursework offerings, enabling far more than just two sets of courses.
I'm sure you won't be on board with this, because it's de facto segregation. It's an option that can be done today and is better able to offer appropriate challenges to students of all abilities.
I will take an option that serves the goal I consider of overriding importance over an uncertain rejection of a known solution with no other options on the table. I am hesitant to trade-off this primary goal via rejection of known methods to advance it in the interest of... let's go with the euphemism "encouraging peer instruction".
As a result, I believe that what you describe does not work.