Why not teleport instead of taking a transport?

In-universe, this is (sorta) covered in the film's official novelisation. The ship is being supplied with a wide range of consumables at far shorter notice than was expected. Presumably the transporters are otherwise occupied moving cargo that's too heavy (or large) to fit onto the shuttles, leaving the shuttles to physically carry the crew from the surface.

The source of those responsibilities appeared not long after the shuttle cleared the ionosphere: the immense orbiting facility that was Starfleet dock. As the shuttlecraft slowed on approach, Kirk was able to pick out his ship waiting in place. Like worker ants attending a queen, a swarm of small support craft darted silently around her, preparing and supplying her for imminent departure. A small smile creased his face. There were other ships in dock, but like anyone thoroughly smitten, he had eyes only for his beloved.

Out of universe, the scene was almost certainly written as a 'walk-n-talk' so that Spock, Bones and Kirk could have a expository conversation about the mission (and then be interrupted by Carol Marcus) without having to explain why they're all sitting around on the ship having a conversation instead of working with their respective departments, getting ready to set off.

It also serves as a "ship porn" shot, allowing adoring fans to gain a well-lit view of the exterior of the ship from multiple angles. This is something which is common to most trek films and almost certainly drew its inspiration from the infamous drydock scene in Star Trek: The Motion Picture