The way I understand it...
Originally, CC was generally for criminals and other people of questionable integrity. Carrying a gun did not cause shame, and those who carried had no reason to hide them. None of that tacticool BS about "element of surprise". If you had a gun, you openly carried it, and that was how it worked.
This also allowed the citizens to know who was carrying and who was not. The town drunk who hasn't seen sobriety in 30 years would know not to carry a gun openly because hey, everyone would know, and someone would probably do something about it. Looking at the underbelly of our history, though, a black person also would know not to carry a gun openly because he would certainly be disarmed. But essentially, open carry lets everyone know who's carrying and who isn't, and eliminates the need for a background check. If someone is a "prohibited person", so to speak, the public makes sure he doesn't carry a gun.
Thus, in a society where open carry is commonplace, and only criminals conceal their guns... you better have a damn good reason for being able to legally conceal a gun. Because really, what is the purpose? Hence why many people don't have a problem with licensing for concealed carry so long as unlicensed open carry is available. Of course, this ignores the issue of how it's impossible to know when someone is concealing well, so CC licensing is pretty much unenforcable unless someone is arrested on another charge. It also doesn't reflect the reality of an anti-gun public that necessitates we CC from time to time to avoid being blacklisted form certain establishments.
As for the second amendment argument, it protects the right to bear arms... it doesn't specify how. And if we look at intent, at the time the document was written, I think we can say the founding fathers didn't intend for people to stash away their guns under heavy clothes. This also goes along with how the second amendment isn't about self-defense, but rather about revolution. I tend to think the founding fathers would rather we carry an AR-15 slung over our shoulder than a little 9mm hidden in a rectal holster. Handguns in general contribute little to "the security of a free State", and I'd go so far as to say that handgun ownership might not be protected by the second amendment... but in the same breath, I'd say that machine guns, rocket launchers, and sawed-off shotguns are thusly protected. Before I get flamed for that, I'm looking at it from a tyrannical-government-resistance point of view. Like I've said, the second amendment isn't about stopping the mugger, unless the mugger is acting as an agent of the government (cue IRS comments).
That's also a valid point that because the second amendment doesn't specify a mode of carry, it must cover all modes of carry. That is, first amendment protections of free speech don't specify the ability to transmit speech over airwaves freely, but we still acknowledge that the protection is inclusive of all modes, and doesn't let the government pick and choose which modes it allows. Then again, this echoes the cries of those who choose to believe the Constitution is a "living, breathing document" that can be edited to reflect modern realities, rather than trying to change the modern realities to fit the Constitution.
So in a long-winded way, that's
the historical basis for restricting CC while protecting the right to OC uninfringed.
As for where I stand, I'm split. I don't really care about concealed carry rights so long as open carry rights are protected. However, we're not there yet. And ignoring concealed carry rights in order to pursue expanding open carry rights could lead us to shooting ourselves in the feet, so to speak, in the event that restrictions on CC advance faster than expansion of OC. And it also does nothing to change the hearts and... lack of minds of those who have a jihad against guns. That is, even if anyone not currently in prison or mental hospitals were, overnight, allowed to open carry any gun, anywhere in the United States, while completely banned from carrying concealed, many people would be fired from their job for OCing a gun where they would still be employed if they continued to CC. There's also the issue of how a ban on CC could be abused to prosecute people who accidentally cover parts of their guns. And then there's that hairy issue of how criminals are going to keep concealing anyway. So I accept concealed carry for right now in history, and will fight to protect the peoples' right to do it uninfringed, even if I don't necessarily agree with it.