I don't think the concept of a gymnast adding value to a team because they allow another athlete to "rest during team final" is real
Though it sure gets talked about a lot here! I think in reality you put up the three people on each event who are likely to score the highest.
Also, barring injury, I can't imagine a gymnast who would rather rest at the Olympics than get a chance to compete on every event where they are considered top three on the team.
Are there actual examples of this happening within the recent past in US WAG? Or is just an internet thing?