While 2nd Amendment advocates certainly claim bearing arms is a right, the “gun control” issue to me is really more about “prior restraint.”

This would be true in the US as well as many other countries. Consider this first; can we agree that in most countries the number of law abiding citizens who legally own guns typically heavily outnumbers those who use guns to commit crimes? This would exclude countries that have total gun bans, such as Japan (and Japan’s societal attitudes towards personal weapons ownership date back thousands of years and made a total gun ban fairly easy to implement).

If so, then the following is at the root of the world view of the two sides of gun control:

Gun Rights Advocates: As a free person you are considered innocent until you prove yourself otherwise and are trusted to inherently respect the rights of others and would only use firearms if necessary in self defense. (I would posit this applies to most people)

Strict Gun Control Advocates: You are to be considered untrustworthy and absent laws and strict enforcement will not inherently respect the right of others and would use firearms inappropriately. (I would say this almost universally applies to criminals, terrorists, insurgents, etc)

Criminals, to include terrorists and insurgents, tend to not obey the laws of the state so gun control laws will not prevent them from acquiring or using guns in criminal activity. The police and/or security forces cannot be everywhere all the time; that is unless you create a police force that is virtually 1 to 1 to the citizenry. That is both unfeasible from a fiscal standpoint and from the view that it would literally create a “police state.” So while “To serve, and protect” is a nice motto for many law enforcement agencies; the reality is an emphasis heavily weighted towards “serve” rather than “protect.” In fact most US courts have found the police have "no duty to protect" an individual citizen. They protect by removing criminals after the fact, thus "protection" come under the rules of law in the form of dissuasion to not break laws through the penalties for the inappropriate use of guns.

“Gun control” is just one of the several issues concerning a state's control over its citizenry. In a free society the state should limit its control over individual activity and restrict itself to advising the citizenry of potential danger or punishing those who do grievous harm. For example, I have no problem with warning labels on alcohol and tobacco products or even the government requiring McDonald’s to put caution “high saturated fat content” warnings on its Double Quarter Pounder with Cheese wrapper. But the government has absolutely no business telling me I cannot drink, smoke, and consume Micky D burgers all day long should I choose to. Or that I cannot own guns.

So one of the effects of criminalizing what was previously a legal activity, whether in COIN or in societies in general, is that there will be those who willfully disobey the law by possessing guns, preferring to feel secure and willing to suffer the consequences if they must use the weapon in self defense.

Another effect would probably be the expansion of an underground market for weapons, particularly if the security situation is poor and police and security forces unable to adequately provide security. This expansion of illegal activity would no doubt prompt a response from law makers and law enforcement thus adding to their responsibilities. As to what order of magnitude these would take on would depend on other factors such as the pre-ban number of weapons, the overall level of personal security, and the size of the security forces in relation to the security level.