As a retired Army soldier, I can tell you that nothing happens quickly or effectively once it is filtered through the government. Superheroes act with quick decisions and morality, neither a government strong suit.
Will S.H.I.E.L.D. make them take on cases they don't want to pursue? Conversely, will S.H.I.EL.D. prevent them from taking on a crime (perhaps insisting another hero is better suited for the job)?
I only forsee complications and negative effect of this government intervention. No superhero needs to be registered to do their job.