I don't get preferring that Starfleet Intelligence do what Section 31 does. Doesn't that make Starfleet the same as Section 31? I prefer they be kept separate.
Before someone says, "I prefer they don't exist!" That ship has already sailed... It's in New Trek, Old Trek, and one of the films.
It's not a question of wanting SI to be exactly like S31. It's just that there are two possibilites:
Either S31 is still just as bad or close to as bad, in which case, making them overtly sanctioned is problematic in all kinds of ways. The story would be far better served by just making the story officially about Starfleet Intelligence and then including some agents among the cast who are secretly S31, because a setup like that would allow you to tell exactly the same sort of story without any of the same issues and would enrich the narrative possibilities to boot.
Or S31 is not as bad, or maybe it could be or couldn't be, like the story is about a fight for the soul of S31 or something similar. In that case (especially in combination with the totally overt operations), you've just retconned everything that made S31 what it is out of existence so there's really no point even using the name. Might as well just call it Starfleet Intelligence and leave some possibilities open for the future.