One man's honey was another man's poison.
The Tesseract, which SHIELD, Loki, and the Chitauri fleet all valued, was a hot potato for Luke.
It was only right for him to throw it away.
If he couldn't put it in his inventory, it was like a ticking time bomb — not only could it explode at any time, it could also be remotely activated.
He would only get himself killed if he held onto something that he couldn't control or use.
SHIELD had no objections either.
No matter how unwilling he might be, Nick Fury, who had almost been killed because of the Tesseract, didn't dare let it remain on Earth.
Earth truly might not be able to survive another invasion via the Tesseract.
The bald director hadn't mentioned keeping the Tesseract. Clearly, he shared Luke's thoughts.
So, in the evening after the battle, Thor took the Tesseract and escorted his baby brother back to Asgard, saying that he had to deal with the Tesseract as soon as possible.