I agree with you that something needed to be done to restore order, but there's a difference between simply telling the public what they want and following through with those actions.

For example, Rossiu could have easily held a public trial, found Simon guilty and then say that Simon was executed to satisfy the mob. I'm sure with all their technology they could have easily faked a convincing video of Simon being executed, while in reality, Simon would still be alive behind the scenes, helping out with the crisis. Rossiu could have even made an announcement to the public that a new pilot was found for Gurren-Lagann so that Simon could continue using it (since it is the best weapon they have, there's another of Rossiu's bonehead moves when he said he wanted it scrapped).

I realize he had to do something to restore order to Kamina City but I simply think he went completely about it the wrong way.

(and don't get me started on that stuff where he was forcing people who wanted to stay underground to the surface because I agree with Viral in that those actions were no different than the Spiral King's)