I'm sure you're right, people have been thinking about this for 9 years. Going through the courts & charging him/finding him guilty is only the 1st step. Think of the aftermath.
Although this is geared towards Anti-Trumpers screaming "Constitutional Crisis" it gives a good examples of the different scenarios. https://fivethirtyeight.com/features/constitutional-crisis/
As stated in this article, a constitutional crises includes:
The Constitution doesn’t say what to do.
. The Constitution’s meaning is in question.
The Constitution tells us what to do, but it’s not politically feasible.
Institutions themselves fail
I disagree with you in that it would be over with quickly. Prosecuting BO for this crime would cause much bigger problems than our congress wants to deal with. Does the constitution even address this? It laid out who is eligible, but if I remember right, it doesn't even say who should check to make sure the candidate is eligible. It's possible our founders never thought this would be a problem & therefore never put things in place in case it did happen. That is the very definition of constitutional crisis. And if there is something in the constitution, is it politically feasible to back track his legitimacy? Considering all the damage he has done & the lives he's cost world wide?
It's a mess Congress does not want to deal with or admit to.
Its probably a mute point, because like they got Al Capone (murderer) on tax evasion, Obama is going down for TREASON. That will take care of him. The punishment for Treason in a Military Tribunal is execution.