It's a cost saving choice that they have sold to you as a design choice. and FPS is a genrebreh first person games exist in damn near every genre lol... and there is no direct participant/viewer interactivity with movies so framing immersion from that perspective consistently pushes people away and always has.
1st/3rd in games are a design choice. and if you want to see the effects plainly just look at the reactions of people playing RE games from different perspectives. those games can hit very different based on how you're allowed to steer action