I think that if this government had a leader, or leaders, that were very smart at leading people and putting programs in place that would make a country boom both economically and keep the people happy, then of course they could make a society that has all of these things.
The media has created a great perception over the years based around government political corruption. The government has been involved in a lot of public concerns over the years and it is only going to get worst overtime. There has to be many steps taken involving modern society to restore social order of some kind.
The issue with modern society and the advent of 24 hour instant news is that people have access to the governments most intimate secrets immediately, whether they be true or false. The media has created a paranoia that borders on hysteria when it comes to government corruption and subversion. The government, both state and federal, have certain dealings which, in the interest of public opinion, must remain secret. These secrets are necessary. However, the integrity of those secrets often get exposed during a paranoia infused investigation that is figuratively stabbing in the dark. There is something to be said of the corruptability of the shadow regime, but ours has been corrupt since the beginning of the country, and we made it this far. I think the proposed system could be very effective in all areas listed, provided the shadow regime enforces the values of the nation as opposed to the morals of a few people who think they "know best."
Shadowy, joint rule by a select few could actually work and work very well. The thing is is that you need a specific group of people to do this. And it would have to be some of the best and brightest in the world. Like, perhaps, scientists. So yes, it's plausible.
Government selected & controlled by a wealthy elite through secret deals, donations and patronage or powerful lobbyists for industry groups will ONLY look after it's own interests. What about everyone else? If their rights aren't defended they become the plundered feudal underclass.
We should go back to a true representative democracy that is open & transparent.
I don't think you can have a joint ruling system that has someone in the shadows. Its going to be very hard to not butt heads. I think any system that has these issues in place isn't going to show good favor to the people. I would just think the political figure is a puppet.