This is a complicated question, made more difficult because there are few laws which support Superman taking the technologies from where they fell.
Given the issues surrounding the military invasion of Earth by the Kryptonians, most Human governments would view anything falling into their hands as a result of those actions as the spoils of war. If Superman were to take said technology from those governments, through his physical might, those governments would be legally capable of declaring war on him, since he would be removing what they are claiming is now their property.
- Each place where the Kryptonian technology fell is technically within a particular country's jurisdiction, and this would legally prevent Superman from taking that technology without violating these laws or policies.
Since Superman has no legal right to any of the technologies (he is not the owner, nor the creator of said technologies) and there are likely no laws which would cover him being the sole survivor of his species.
With time and a dedicated legal team, perhaps some provision could be made for him being able to claim those technologies under a cultural precedent, as the last survivor of a dead intelligent species.
But without exercising his power purely as a sovereign state, those wrecks belong to the governments where they fell, to do with as they please, exercising some variant of "the law of salvage" under maritime law.
- The law of salvage is a concept in maritime law which states that a person who recovers another person's ship or cargo after peril or loss at sea is entitled to a reward commensurate with the value of the property so saved. The concept has its origins in antiquity, with the basis that a person would be putting himself and his own vessel at risk to recover another and thus should be appropriately rewarded.
- A related consideration was widespread piracy; a vessel in peril could very well be left for pirates if the owner did not generously reward a potential honest salvor.
- Salvage law has been recognized for centuries in such documents as the edicts of Rhodes and the Roman Digest of Justinian. It is still a nearly universally recognized right, though conditions for awards of salvage vary from country to country.
Given the fear and loathing the Kryptonians engendered with their failed attempt to take over the Earth, it was probably inadvertently wise of Superman to avoid becoming embroiled in politics over the Kryptonian technology. It could only create ill-will and given the overall demeanor of people during Batman v. Superman, it certainly wouldn't have helped.
The fear the Human populaces had could have only been inflamed if he had decided to gather up every scrap of said technology and hid it in a Fortress someplace inaccessible to Humans. Having no serious experience with said technology himself, he might not have been aware anyone would be able to use it and perhaps thought there was little humanity could learn from it. A reasonable mistake to make considering his Earth-raised heritage.
There is one other thing to consider, we don't know how much Kryptonite might be remaining in any of these wrecks, so we don't know if Superman had tried to raise them only to find himself weakened and unable to do so.