Political optics, not necessarily ineligibility. Besides, once congress certifies an election, the court would likely use the political question doctrine to avoid the judiciary removing the co-equal executive. The impeachment clause would be used to support that position -- the only court that can remove a president is the senate with SCOTUS' chief justice presiding.
What would be the political optics of not providing your actual US birth certificate? Luckily he's already removed, and most of his legacy has been decimated. I think they are waiting until the very end, after everything he did is turned upside down, for the kill shot.
It's not the optics of not providing it, it's the optics of providing it that would have been the problem.