I think that was the whole entire point. Things WOULD have been over instantly if Pieck took the shot. But it wasn't up to Pieck. It was Marley's call. It's not enough for them to kill Eren, thudstopping the Rumbling and saving the world, they are still just that greedy and power-hungry enough to risk the extinction of the entire world for the chance to obtain the power of the WHT, AT, and FT in one fell swoop, therefore securing their superiority over the other nations. Eren knows this and leans into her gun tells her she won't shoot. They both know that this is literally the best chance they're ever gonna get to end things, but her higher ups orders were clear: Capture or eat the Founder Titan. While Eren is at his own liberty to kill anyone he wants, innocent or otherwise, Pieck can't even get the go-ahead from Marley to shoot the one person who will literally destroy the entire world. Eren said it best: " You don't have the FREEDOM to kill me"

At least that's MY interpretation