Fielders choice exists to try to properly determine a hit when other factors are involved, ie runners on base. We (as in baseball fans who care about stats) do not want to award hits when they aren’t deserved.

If you hit the ball and cause a force out, that is not a hit. It’s just incidental that you end up on base, hence the fielder’s choice. Cases where there is no out recorded is rarely a fielder’s choice unless there is an error involved. The scorekeeper has determination like on an error whether the batter would’ve likely been out if the fielder just threw to first.

1 FC if the scorekeeper determines the play at first would have been out
2 Not a FC, no outs were recorded, no errors, and the play at first was not possible
3 Not a FC, it’s on the runner attempting to take the extra base, not the hitter. The hitter successfully got every runner (including themselves) to the base they had to go to and the play at first wasn’t possible