The federation has no power to make skaters skate one or both events. What are they going to do if they refuse? Kick them off the team (also known as cutting off your nose to spite your face)? And why would the USFSA want to force a skater to skate if he didn't want to?
For the last time, the federations have ALL the power, in terms of the rules. They decide the entries to any competition. No athlete is allowed to compete anywhere without federation approval and they can be withdraw from a competition at any time if the federation wants.
USFS shouldn't have to "force" anyone. The skaters are on the team to do a job. Their job is competing, in the way that best serves the team.
Regardless, it's similar to a Parent-Child relationship. Just because a child doesn't want to clean their dishes, that doesn't mean they should be allowed to make the house worse for everyone. There are many things children (or people of any age) don't want to do, but
should do, for their own best interest and the good of the community.
If the skater refuses to compete after being declared the entry, then they screw the team over. Sure, they can make that decision if they want, but the blowback would be immense, and they would be throwing an Olympic medal of their own away. Who would do that?
WHY on earth he’d risk his injury worsening and having to peak four times under immense Olympic pressure?
He has no kind of medical issue that would be worsened by doing the Team LP and he doesn't have to peak four times. Again, he can skate watered down content in the Team LP and still win the segment, because of how favored he is by the judges. There is no greater risk of injury than doing a normal practice program. Which he will be doing every day at the Olympics. So on the day of the Team LP, he can do his practice session in the competition rink instead of the practice rink. It's really that simple.
Also, if doing the Team LP really is an impediment to a skater's individual event, then inherently whoever is placed there is being screwed over. In which case, USA is only hurting their medal chances even further by placing Vincent in that segment. The goal of a federation should be obtaining the maximum medal haul. USA could potentially win Gold in the Team, and Gold + Silver in the Men's event. If doing the Team LP is sooo difficult, then Vincent's individual medal chance is now being hurt in ADDITION to the Team Gold chance. Whereas I would argue Nathan is SO far ahead of the field (in terms of the judging, at least) that he is extremely likely to win the individual event anyway, even if faced with the "imposition" of needing to do the Team LP. Although it's not actually an imposition.
For a major reality check - Male gymnasts compete 6 events in a single day at the Olympics, and they do this in a qualifying round, and then a team round, and then an individual round, all of these competitions taking place over the span of 4 days, and then after all that they also have event final rounds a few days later! It's absolutely laughable to suggest figure skaters can not successfully compete 2 SP's and 2 LP's over the course of a week.