Abraham Lincoln was a God fearing president that's why he became the greatest president of America. Skills must be tempered with genuine passion to serve the country in order to be a good president. Skills alone won't do anything good for the country. As what happened to our country and other countries whose presidents have the necessary skills but lacks genuine passion and heart to serve their constituents. The flaw in your premise is that one must believe in God in order to have the kind of heightened passion, heart, etc to run a country.
There are people who truly and sincerely believe in God, and believe that their good traits are derived from their faith. If that works for them, fine. But it's very presumptuous (and also wrong) to maintain that the traits you describe only exist in God fearing people.
And I disagree that skills alone won't do anything for the country...skills and logic and experience are PRECISELY what is needed.
As for religion in general, I think most people pay lip service to it, and believe in God because they are scared sh__less not to. You can put all the faith you want into the after-life, but in THIS world, I know you look both ways before you cross the street. :)