I didn’t see the most important of action’s i.e verify given. The past elections might demonstrate those criterion that you listed but as to cases like Obama these alone do not encompass a valid eligibility. An ‘examination’ can be faulty or colored, a ‘consideration’ can be shallow or misdirected, and ‘approval’ can be bought or forged and I can agree all three point words apply to Obama. ‘Verify’ was certainly missing.
The Constitution does not and cannot guarantee that there will never be any mistakes made by those who are charged with making the decision as to a presidential candidate's qualifications. No matter who is charged with making the decision (whether it be the voters and their electors, a court or some committee), errors can be made. A proposal to turn the matter over to a court is not a proposal to eliminate all possibility of error.
Our Constitution empowers the voters and the their electors to select our presidents. It does not empower courts to try to interfere with the process by attempting to become a "Qualifications Committee."
For 57 elections in a row, the voters and their electors have chosen our presidents without any court even once attempting to interfere by attempting to disqualify a candidate because it felt that a candidate might not be qualified. The courts have not so interfered and they will never so interfere because they have no constitutional basis for doing so.