(1) It is not the responsibility of anyone but BO & the Demonrat Party to prove that he is qualified. (The Constitution does not say, "Anybody can be President as long as no one else can prove that they're not qualified.")
(2) The government should have no dog in the fight, therefore should not be a party to case, therefore should collect no expenses, regardless the outcome.
Otherwise, I think that's a fine idea.
And the Constitution fails to provide a process by which the president’s eligibility is verified.
And there is no law that state’s that this president must provide more documentation than any other president in history.