It is important for this story that Fingolfin be the one to decide to go to the harbor to 'rescue' the Noldor. While Fingon can be eager and with him, he can't really be the one to make the explicit decision to rush into the battle. In a chaotic situation, might it happen that way? Sure. But we need Fingolfin to make the choice as a leader, not a follower. Fingolfin will feel responsible for leading his people into the Kinslaying after the fact, causing him to break his sword. Fingon will (eventually) come to feel guilty for his own actions, but he's not going to take on the collective guilt of the Noldor. We'll have plenty of opportunities to explore his role as a leader, and he clearly does act independently (such as when he rescues Maedhros).
Right now, the story is mostly about Fëanor and Fingolfin being in very uneasy alliance. We are building up to Fëanor's betrayal of Fingolfin when he burns the ships. The friendship of Maedhros and Fingon was established in Season 2 (when they were still young), and we heard both of them speaking with one another about the family drama in an attempt to see how to solve it all. But by the time Fëanor was banished from Tirion, they were not being fully open with each other (especially on Maedhros' part), and we did not really show their friendship much after that. So their story is certainly part of all of this, but right now they're mostly keeping separate from one another. Not exactly estranged, but not exactly working together as a team, either. So, Fingon's desire to rush into the Kinslaying because of Maedhros is there as a motivation, but it's not the most important aspect of all of this - it's just a personal thing on the side.
And while Turgon could just be 'at the back of the line' and therefore not realize there is any decision to be made, that does feel like we're just forgetting about him, rather than actually differentiating him from his father and brother. And if we're not going to show any difference anyway...he might as well be with them. There's a lot of different ways to do this, and I don't mind variations, but if we're going to make explicit choices, I like for there to be a story behind them. So, if he's at the back of the line, the reason would have to be something along the lines of looking back at Tirion, or Idril being too little to keep up, or Elenwë in tears after they pass through the Kalakirya because she's never been that far from Taniquetal before, or....*something*. If we have a reason for it, it can fit into the story. But just not showing him because he stopped to tie his shoes and missed the Kinslaying wouldn't really work (not that anyone has suggested that, but just...we need a reason/story).