The GC riders become that when they have earned it. The team believe that they're have the best chance of winning out of all the team members, so they organise the team to give him the best chance. Often they crash out in the race, some the team has to come up with plan B and give someone else a chance. If there's two guys in the team that both show they have potential to win, the chances are that one of them will be poached by another team at the end of the season. It's the same in Formula 1. There's normally a preferred championship winner.
This Tour de France racing is more exciting than F1 because there's a lot more going on with the tactics and interrelationships as well as the skill of the rider in racing down slippery windy roads at speeds of up to 70 mph on skinny tyres with rim brakes. F1 would become more similar to bike racing if there were say 6 drivers in each team. That would make it interesting.
Don't forget also that in the TdF, there's two time trial days, where the riders are completely on there own. That's where they make the biggest time differences, so your GC rider has to be the best racer on his own with the ability to at least keep up with the best on the long hill-climbs and have the stamina to be able to sprint at the end of a 200km ride.