My understanding is Sweden's "SEC" (in US terms) is called Finansinspektionen. Wouldnt this EU commission be like the Finansinspektionen issuing a fine or revoking a license if a bank didnt comply with regulations? My understanding is the Finansinspektionen can do this sort of thing but has to go to the court for larger actions.
Perhaps the EU commission has a bit more leeway?
The European Commission is both the executive and legal branch. They propose the legislation that the European Parliament can only approve or reject. On the other hand, the European Patliament can not propose anything at all.
While I agree this should ideally also be available to the EP, it doesn't make the EC a legislative branch. It's very much the executive.
The Commission is elected by member states and thus represents them indirectly.
Law comes from parliament alone, and the constitution does not permit for the executive (regeringen) to intervene in individual cases.