Rather than spend 100,000s of thousands of dollars to obfuscate and produce the birth certificate and it all goes away.
And then what? In a way having the question out there is to his advantage. Perhaps he has the proof but wants to keep his political foes occupied.
Even now there is not a lot of coverage on this issue and any attention given to this is watered down or excused away by the msm. Meanwhile his foes argue amongst themselves over his legitimacy, which offers the opportunity for the media to casts his foes in a negative light.
Should matters get out of hand, he can produce the evidence and thumb his nose at his detractors with little to no damage to himself. If anything, with the help of the media, he may even come out looking better for it.
Or then again, maybe he is hiding something and that is why his administration and congress are fast at work on so many changes before the gig is up.
Bingo!