The De Facto Officer Doctrine is well established and legitimizes decisions made by someone later found to be holding office improperly. There’s no doubt.
The country is fractured over the results of a completely legitimate election. You are denying reality if you think proving Obama a fraud wouldn’t be 100 times worse.
The de facto officer doctrine confers validity upon acts performed by a person acting under the color of official title even though it is later discovered that the legality of that person’s appointment or election to office is deficient. Norton v. Shelby County, 118 U.S. 425, 440 (1886). “The de facto doctrine springs from the fear of the chaos that would result from multiple and repetitious suits challenging every action taken by every official whose claim to office could be open to question, and seeks to protect the public by insuring the orderly functioning of the government despite technical defects in title to office.” 63A Am. Jur. 2d, Public Officers and Employees § 578, pp. 1080-1081 (1984)
You need to look a little more closely at the case law than Am Jur in order to understand the limitations on the operation of the doctrine.
The doctrine does not apply if the officer is not eligible to hold the office as distinguished from situations where the defect in the claim of authority is attributable to the election or installation process.
I have not looked at the question with respect to the Senate seat. The requirement for a senator simply is that he be a citizen of the state he seeks to represent. You might assume that is an eligibility test which implies a requirement of citizenship in the US to be a citizen of the state but it is not as clear as the Article II Section 1 eligibility requirement for the President.
And with luck, the return on a conclusive Court decision holding Barry was never eligible to serve as President diminishes fairly rapidly now.
Many of his acts in office were legal even if he was not the President. Lots of legislation would have become law even if he had not signed it. Some of his foreign policy acts were signed off by Joe Biden at the insistence of Mrs. Clinton, based on the Constitutional Law opinions of her husband. (If Barry was not the President on eligibility grounds, Joe was acting President under the Constitution.)
The real return on a decision that he was not eligible would be elimination of Sotomayor and Kegan from the Court. Sotomayor has a health problem that is likely to eliminate her fairly soon. Kegan has some other vulnerabilities--when she is gone, most of Barry's legislative record is gone also; no one will care.
The entire affair is just another part of the sordid history of public administration of the United States in the twenty-first century.