My suspicion is that given a choice between requiring that people who carry do so openly, or requiring them to carry concealed, many politiciains would rather requirement concealment.
Once again. What "many politicians" would rather is absolutely and utterly irrelevant. Nor is the issue of "open carry" vs. "concealed carry" germane. The only point of relevance is that the citizen's right to keep and bear arms is a God-given right with which the government has no business interfering. Indeed, the very notion of "the government" intruding in the matter perpetuates the mistaken notion that governments exist to regulate citizen activity. Or that they may do so. They do not and they may not, except as specifically and explicitly detailed in the Constitution. That is the purpose and import of Article X.
The ONLY point that bears on the question is that governments exist at sufferance, solely "to secure these rights", "deriving their just powers from the consent of the governed", and to protect the rights of the people is the sole purpose for which "Governments are instituted among Men."
That's it. That's all there is. It's not rocket science. It's not even complicated. "Shall not be infinged" means exactly and precisely what it says. Anything which purports to equivocate with respect to that is simply dishonest, legalistic sophistry.
Alas, the nation is awash in dishonest, legalistic sophistry - and has been for more than fifty years. The genius of the Founders was to design a fool-proof system of checks on the power of government and balances in power between its different branches. What they failed to anticipate is that when anyone designs a fool-proof system, society simply provides bigger fools.