"Launching from the Earth's surface requires a huge amount of energy, and it's been stated that it wasn't done."
This appears to be the key to the nerd rage. If Starfleet didn't build the craft on Earth then showing them in the new movie being built on Earth is a mistake. But it's not a question of physics.
Yes, I agree completely. The first part of my post was expressing why I found the question about approaching Earth misguided, irrelevant, or inappropriate. Clearly the Nerd Rage is just about the inconsistency with the "earlier" episodes.
The comments about the physics also sparked a conversation about escape velocity here in the office. It's easy to compute that orbital velocity at grazing altitude is about 8 km/s. People confuse that with escape velocity, which is sqrt(2) faster, or about 11.3 km/s.
The real confusion arises in that a craft never needs to reach escape velocity to escape. You can happily escape without ever travelling faster than 6km/hr - walking pace.
If this confuses you, it's fun to work out why. And how. And why NASA doesn't do that. The sums are fairly easy, it's the conceptualisation that's hard.
This appears to be the key to the nerd rage. If Starfleet didn't build the craft on Earth then showing them in the new movie being built on Earth is a mistake. But it's not a question of physics.