Why aren't S.H.I.E.L.D. founders simply stripping Coulson out of power formally?

In the recent episode of Marvel's Agents of S.H.I.E.L.D. TV series, we came to know about the real S.H.I.E.L.D. The founders don't like Coulson because he is following the same path as Nick Fury and he isn't same after he was injected with alien DNA. That's fine. But, why aren't they simply stripping Coulson out of power officially after introducing themselves? If they think Coulson would resist, then they can always do it hard way. I don't think Coulson's S.H.I.E.L.D. (which has financial problems) can stand a chance against real S.H.I.E.L.D. (which has a Helicarrier). Talking about Fury's cube, there's no point in searching Coulson's office with a toy car if you know the location. After crushing the band S.H.I.E.L.D., the room can always be searched in a better way. Why exactly is the real S.H.I.E.L.D. playing monkey?