Sorry to be contrary, but it's not good for kids to feel being smart is their
identity, talent, and self-worth. Basically, if your identity is wrapped up in your smarts, which you can't control, then when your smarts aren't enough (i.e. college, big test, tough subject), then you crumble and can't cope and lose self-worth. If your identity is wrapped up in your work ethic, then you always feel you are in control, even when things get tough.
This is a REALLY big problem for gifted kids who are constantly told they are smart (that's why I hate that label). They believe their self worth is their smartness. If they are ever not smart enough, they struggle. It's really, really important to develop self identity around work ethic for gifted kids.
This video explains the research on this by Carol Dweck, which has been replicated with thousands of children: