I am always having this kind of discusion in Germany. Germany is a "talent" focused country. The kids have it or don't. That's unfair.
I explain always that "talent" is a journalist's word, for people who doesn't understand how music (or sports or anything requiring complexer brain neuroplasticity) works. As said before, "Talent" is the sume of too many components and the majority of them are not inherited, but they part of environment. When looking for kids best options, look for what really absorve their attention. That's the best guess.
Did you know that many kids that were told by teachers "you don't have the talent for the trumpet, maybe try another instrument" were probably up stream players?! The teachers were in old times not so good informed as now.
I'm not a chops doctor nor a troubleshouting teacher, but I have a lot succes with both young and adult students who were jus told "to quit" by other teachers. You have to have patience and analyse where the problems, the frustration and the possible ways of improvement are. Every person is a world. That said, in most cases, the problem is mental. A teacher or themself thinking, they can't play. That makes me very sad.
I was part of a study abot focal dystonia in brass players here in Munich (my wife is neurologist). I was in the control group (that's the healthy ones) and they scanned my brain. If you practice music for more than 3 hours a day, from 7 to 10 years long, your brain (connections firing, amount of neurones, fat Myelin placement) has changed so much, it doesn't like like a non musician brain. It's pretty beautiful to look at it. I got it in DVD.
Neuroplasticity is key. Only sad thing about it, it get slower with age. But you can still always improve! It takes just longer!
(sorry for the length)